A Viscoelastic Model for the Long-Term Deflection of Segmental Prestressed Box Girders

Most of segmental prestressed concrete box girders exhibit excessive multidecade deflections unforeseeable by past and current design codes. To investigate such a behavior, mainly caused by creep and shrinkage phenomena, an effective finite element (FE) formulation is presented in this article. This formulation is developed by invoking the stationarity of an energetic principle for linear viscoelastic problems and relies on the Bazant creep constitutive law. A case study representative of segmental prestressed concrete box girders susceptible to creep is also analyzed in the article, that is, the Colle Isarco viaduct. Its FE model, based on the aforementioned energetic formulation, was succ…

Wave propagation in 1D elastic solids in presence of long-range central interactions

Abstract In this paper wave propagation in non-local elastic solids is examined in the framework of the mechanically based non-local elasticity theory established by the author in previous papers. It is shown that such a model coincides with the well-known Kroner–Eringen integral model of non-local elasticity in unbounded domains. The appeal of the proposed model is that the mechanical boundary conditions may easily be imposed because the applied pressure at the boundaries of the solid must be equilibrated by the Cauchy stress. In fact, the long-range forces between different volume elements are modelled, in the body domain, as central body forces applied to the interacting elements. It is …

The Multiscale Stochastic Model of Fractional Hereditary Materials (FHM)

Abstract In a recent paper the authors proposed a mechanical model corresponding, exactly, to fractional hereditary materials (FHM). Fractional derivation index 13 E [0,1/2] corresponds to a mechanical model composed by a column of massless newtonian fluid resting on a bed of independent linear springs. Fractional derivation index 13 E [1/2, 1], corresponds, instead, to a mechanical model constituted by massless, shear-type elastic column resting on a bed of linear independent dashpots. The real-order of derivation is related to the exponent of the power-law decay of mechanical characteristics. In this paper the authors aim to introduce a multiscale fractance description of FHM in presence …

Advanced microscopy analysis of the micro-nanoscale architecture of human menisci

AbstractThe complex inhomogeneous architecture of the human meniscal tissue at the micro and nano scale in the absence of artefacts introduced by sample treatments has not yet been fully revealed. The knowledge of the internal structure organization is essential to understand the mechanical functionality of the meniscus and its relationship with the tissue’s complex structure. In this work, we investigated human meniscal tissue structure using up-to-date non-invasive imaging techniques, based on multiphoton fluorescence and quantitative second harmonic generation microscopy complemented with Environmental Scanning Electron Microscopy measurements. Observations on 50 meniscal samples extract…

Recent dolomite in playa lakes of the central Ebro Basin, Spain

Contrasting probabilistic and anti-optimization approaches in an applied mechanics problem

Probabilistic and non-probabilistic, anti-optimization analyses of uncertainty are contrasted in this study. Specifically, the comparison of these two competing approaches is conducted for an uniform column, with initial geometric imperfection, subjected to an impact axial load. The reliability of the column is derived for the cases when the initial imperfections posses either (a) uniform probability density, (b) truncated exponential density or (c) generic truncated probability density. The problem is also analyzed in the context of an interval analysis. It is shown that in, the most important near-unity reliability range these two approaches tend to each other. Since the interval analysis…

A generalized model of elastic foundation based on long-range interactions: Integral and fractional model

The common models of elastic foundations are provided by supposing that they are composed by elastic columns with some interactions between them, such as contact forces that yield a differential equation involving gradients of the displacement field. In this paper, a new model of elastic foundation is proposed introducing into the constitutive equation of the foundation body forces depending on the relative vertical displacements and on a distance-decaying function ruling the amount of interactions. Different choices of the distance-decaying function correspond to different kind of interactions and foundation behavior. The use of an exponential distance-decaying function yields an integro-d…

A mechanical picture of fractional-order Darcy equation

Abstract In this paper the authors show that fractional-order force-flux relations are obtained considering the flux of a viscous fluid across an elastic porous media. Indeed the one-dimensional fluid mass transport in an unbounded porous media with power-law variation of geometrical and physical properties yields a fractional-order relation among the ingoing flux and the applied pressure to the control section. As a power-law decay of the physical properties from the control section is considered, then the flux is related to a Caputo fractional derivative of the pressure of order 0 ⩽ β ≤ 1 . If, instead, the physical properties of the media show a power-law increase from the control sectio…

STOCHASTIC ANALYSIS OF ONE-DIMENSIONAL HETEROGENEOUS SOLIDS WITH LONG-RANGE INTERACTIONS

Random mass distribution in one-dimensional (1D) elastic solids in the presence of long-range interactions is studied in this paper. Besides the local Cauchy contact forces among adjacent elements, long-range forces depending on the product of interacting masses, as well as on their relative displacements, are considered. In this context, the random fluctuations of the mass distribution involve a stochastic model of the nonlocal interactions, and the random displacement field of the body is provided as the solution of a stochastic integro-differential equation. The presence of the random field of mass distribution is reflected in the random kernel of the solving integro-differential equatio…

Fractional-order theory of heat transport in rigid bodies

Abstract The non-local model of heat transfer, used to describe the deviations of the temperature field from the well-known prediction of Fourier/Cattaneo models experienced in complex media, is framed in the context of fractional-order calculus. It has been assumed (Borino et al., 2011 [53] , Mongiovi and Zingales, 2013 [54] ) that thermal energy transport is due to two phenomena: ( i ) A short-range heat flux ruled by a local transport equation; ( ii ) A long-range thermal energy transfer proportional to a distance-decaying function, to the relative temperature and to the product of the interacting masses. The distance-decaying function is assumed in the functional class of the power-law …

Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES

In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…

Carotid Artery Disease in the Era of Biomarkers: A Pilot Study

The intima-media thickness (IMT) and its irregularities or ulcerations in the common carotid artery (CCA) are useful tools as sentinel biomarkers for the integrity of the cardiovascular system. Total homocysteine and lipoprotein levels are the most commonly used elements in cardiovascular risk stratification. Duplex ultrasound (DUS), associated with serum biomarkers, can be used simply to assess the degree of atherosclerotic disease and cardiovascular risk. This study highlights the role of different kinds of biomarkers, showing their usefulness and potentiality in multi-district atherosclerotic patients, especially for early diagnosis and therapy effectiveness monitoring. A retrospective a…

Fractional-order poromechanics for a fully saturated biological tissue: Biomechanics of meniscus

Biomechanics of biological fibrous tissues as the meniscus are strongly influenced by past histories of strains involving the so-called material hereditariness. In this paper, a three-axial model of linear hereditariness that makes use of fractional-order calculus is used to describe the constitutive behavior of the tissue. Fluid flow across meniscus' pores is modeled in this paper with Darcy relation yielding a novel model of fractional-order poromechanics, describing the evolution of the diffusion phenomenon in the meniscus. A numerical application involving an 1D confined compression test is reported to show the effect of the material hereditariness on the pressure drop evolution.

Stability analysis of a non-local column with non-central interactions

The finite element method for the mechanically based model of non-local continuum

SUMMARY In this paper the finite element method (FEM) for the mechanically based non-local elastic continuum model is proposed. In such a model each volume element of the domain is considered mutually interacting with the others, beside classical interactions involved by the Cauchy stress field, by means of central body forces that are monotonically decreasing with their inter-distance and proportional to the product of the interacting volume elements. The constitutive relations of the long-range interactions involve the product of the relative displacement of the centroids of volume elements by a proper, distance-decaying function, which accounts for the decrement of the long-range interac…

Waves propagation in a fractional viscoelastic continuum

In this paper the analysis of waves scattering in a fractional-type viscoelastic material is analyzed. Such a material involves, in the constitutive equation, the presence of noninteger order derivatives of the strain filed yielding a memory-type behavior of the material model. The presence of such a term has been also justified experimentally reporting the relaxation modulus of polymeric materials, obtained from experimental test, that are well-fitted by a powerlaw of fractional order. Some numerical applications reporting the standing-waves condition of an 1D solid varying the fractional differentiation order has also been reported in the paper.

Probabilistic analysis of non-local random media

Computational stochastic methods have been devoted over the last years to analysis and quantification of the mechanical response of engineering systems involving random media. Specifically analysis of random, heterogeneous media is getting more and more important with the emergence of new complex materials requiring reliable methods to provide accurate probabilistic response. Advanced materials, often used at nano or meso-levels possess strong non-local characters showing that long-range forces between non-adjacent volume elements play an important role in mechanical response. Moreover long and short-range molecular interactions may have random nature due to unpredictable fabrication proces…

Stochastic analysis of dynamical systems with delayed control forces

Abstract Reduction of structural vibration in actively controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-normal delta-correlated random process with delayed control forces. Taylor series expansion of the control forces has been introduced and the statistics of the dynamical response have been obtained by means of the extended Ito differential rule. Numerical application provided shows the capabilities of the proposed method to analyze stochastic dynamic systems with delayed actions under delta-correlated process contrasting statist…

Posterior meniscal root repair: a biomechanical comparison between human and porcine menisci

The aim of the present study was to compare the biomechanical characteristics of posterior meniscal root repair of porcine and human menisci. Methods. In vitro biomechanical testing was performed using 12 porcine menisci and 12 human menisci. All menisci were sectioned at the midpoint of their circumference and mounted on an electro-mechanic testing machine. The posterior root was sutured with three single stitches using a no. 2 non-absorbable suture. All specimens were subjected to cyclic axial loading followed by load-to-failure testing. Displacements were recorded at the conclusion of cycles 1, 100, 500 and 1000. Further, load-displacement curves of each specimen were recorded and analyz…

Stability analysis of Beck's column over a fractional-order hereditary foundation

This paper considers the case of Beck's column resting on a hereditary bed of independent springpots. The springpot possesses an intermediate rheological behaviour among linear spring and linear dashpot. It is defined by means of couple ( C β ,  β ) that characterize the material of the element and is ruled by a Caputo's fractional derivative. In this paper, we investigate the critical load of the column under the action of a follower load by means of a novel complex transform that allows to use the Routh–Hurwitz theorem in the complex half-plane for the stability analysis.

Polybutylene Succinate Processing and Evaluation as a Micro Fibrous Graft for Tissue Engineering Applications

A microfibrous tubular scaffold has been designed and fabricated by electrospinning using poly (1,4-butylene succinate) as biocompatible and biodegradable material. The scaffold morphology was optimized as a small diameter and micro-porous conduit, able to foster cell integration, adhesion, and growth while avoiding cell infiltration through the graft’s wall. Scaffold morphology and mechanical properties were explored and compared to those of native conduits. Scaffolds were then seeded with adult normal human dermal fibroblasts to evaluate cytocompatibility in vitro. Haemolytic effect was evaluated upon incubation with diluted whole blood. The scaffold showed no delamination, and mech…

Exact mechanical models of fractional hereditary materials

Fractional Viscoelasticity is referred to materials, whose constitutive law involves fractional derivatives of order β R such that 0 β 1. In this paper, two mechanical models with stress-strain relation exactly restituting fractional operators, respectively, in ranges 0 β 1 / 2 and 1 / 2 β 1 are presented. It is shown that, in the former case, the mechanical model is described by an ideal indefinite massless viscous fluid resting on a bed of independent springs (Winkler model), while, in the latter case it is a shear-type indefinite cantilever resting on a bed of independent viscous dashpots. The law of variation of all mechanical characteristics is of power-law type, strictly related to th…

Development and characterization of xyloglucan-poly(vinyl alcohol) hydrogel membrane for Wireless Smart wound dressings

Abstract Hydrogel-based smart wound dressings that combine the traditional favourable properties of hydrogels as skin care materials with sensing functions of relevant biological parameters for the remote monitoring of wound healing are under development. In particular, lightweight, ultra-high frequency radiofrequency identification (UHF RFID) sensor are adjoined to xyloglucan-poly(vinyl alcohol) hydrogel films to battery-less monitor moisture level of the bandage in contact with the skin, as well as wireless transmit the measured data to an off-body reader. This study investigates the swelling behavior of the hydrogels in contact with simulated biological fluids, and the modification of th…

Fractional multiphase hereditary materials: Mellin Transforms and Multi-Scale Fractances

The rheological features of several complex organic natural tissues such as bones, muscles as well as of complex artificial polymers are well described by power-laws. Indeed, it is well-established that the time-dependence of the stress and the strain in relaxation/creep test may be well captured by power-laws with exponent β ∈ [0, 1]. In this context a generalization of linear springs and linear dashpots has been introduced in scientific literature in terms of a mechanical device dubbed spring-pot. Recently the authors introduced a mechanical analogue to spring-pot built upon a proper arrangements of springs and dashpots that results in Elasto-Viscous (EV) materials, as β ∈ [0, 1/2] and Vi…

Fractional-Order Thermal Energy Transport for Small-Scale Engineering Devices

Fractional-order thermodynamics has proved to be an efficient tool to describe several small-scale and/or high-frequency thermodynamic processes, as shown in many engineering and physics applications. The main idea beyond fractional-order physics and engineering relies on replacing the integer-order operators of classical differential calculus with their real-order counterparts. In this study, the authors aim to extend a recently proposed physical picture of fractional-order thermodynamics to a generic 3D rigid heat conductor where the thermal energy transfer is due to two phenomena: a short-range heat flux ruled by stationary and nonstationary transport equations, and a long-range thermal …

A non-linear stochastic approach of ligaments and tendons fractional-order hereditariness

Abstract In this study the non-linear hereditariness of knee tendons and ligaments is framed in the context of stochastic mechanics. Without losing the possibility of generalization, this work was focused on knee Anterior Cruciate Ligament (ACL) and the tendons used in its surgical reconstruction. The proposed constitutive equations of fibrous tissues involves three material parameters for the creep tests and three material parameters for relaxation tests. One-to-one relations among material parameters estimated in creep and relaxations were established and reported in the paper. Data scattering, observed with a novel experimental protocol used to characterize the mechanics of the tissue, w…

Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay

Abstract An elastic continuum model with long-range forces is addressed in this study within the context of approximate analytical methods. Such a model stems from a mechanically-based approach to non-local theory where long-range central forces are introduced between non-adjacent volume elements. Specifically, long-range forces depend on the relative displacement, on the volume product between interacting elements and they are proportional to a proper, material-dependent, distance-decaying function. Smooth-decay functions lead to integro-differential governing equations whereas hypersingular, fractional-decay functions lead to a fractional differential governing equation of Marchaud type. …

A mechanical approach to fractional non-local thermoelasticity

In recent years fractional di erential calculus applications have been developed in physics, chemistry as well as in engineering elds. Fractional order integrals and derivatives ex- tend the well-known de nitions of integer-order primitives and derivatives of the ordinary di erential calculus to real-order operators. Engineering applications of these concepts dealt with viscoelastic models, stochastic dy- namics as well as with the, recently developed, fractional-order thermoelasticity [3]. In these elds the main use of fractional operators has been concerned with the interpolation between the heat ux and its time-rate of change, that is related to the well-known second sound e ect. In othe…

Non-local continuum: Fractional Calculus Approach

A non-local model of thermal energy transport: The fractional temperature equation

Abstract Non-local models of thermal energy transport have been used in recent physics and engineering applications to describe several “small-scale” and/or high frequency thermodynamic processes as shown in several engineering and physics applications. The aim of this study is to extend a recently proposed fractional-order thermodynamics ( [5] ), where the thermal energy transfer is due to two phenomena: A short-range heat flux ruled by a local transport equation; a long-range thermal energy transfer that represents a ballistic effects among thermal energy propagators. Long-range thermal energy transfer accounts for small-scale effects that are assumed proportional to the product of the in…

Active controlled structural systems under delta-correlated random excitation: linear and nonlinear case

Abstract Reduction of structural vibration in active controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-Gaussian random process accounting for the time delay involved in the application of active control actions. Control forces acting with time-delay effects will be expanded in Taylor series evaluating response statistics by means of the extended Ito differential rule to consider the effects of the non-normality of the input processes. Numerical application provided shows the feasibility of the proposed method to analyze stochastic …

Digital simulation of multivariate earthquake ground motions

In this paper a new generation procedure of multivariate earthquake ground motion is presented. The technique takes full advantage of the decomposition of the power spectral density matrix by means of its eigenvectors. The application of the method to multivariate ground accelerations shows some very interesting physical properties which allows one to obtain significant reduction of the computational effort in the generation of sample functions relative to multivariate earthquake ground motion processes. Copyright © 2000 John Wiley & Sons, Ltd.

Advanced materials modelling via fractional calculus: challenges and perspectives.

Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can successfully describe complex long-memory and multiscale phenomena in materials, which can hardly be captured by standard mathematical approaches as, for instance, classical differential calculus. Furthermore, fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials. The theme issue gathers cutting-edge theoretical, computational and experimental studies on advanced mat…

Laminar flow through fractal porous materials: the fractional-order transport equation

Abstract The anomalous transport of a viscous fluid across a porous media with power-law scaling of the geometrical features of the pores is dealt with in the paper. It has been shown that, assuming a linear force–flux relation for the motion in a porous solid, then a generalized version of the Hagen–Poiseuille equation has been obtained with the aid of Riemann–Liouville fractional derivative. The order of the derivative is related to the scaling property of the considered media yielding an appropriate mechanical picture for the use of generalized fractional-order relations, as recently used in scientific literature.

The fractal model of non-local elasticity with long-range interactions

The mechanically-based model of non-local elasticity with long-range interactions is framed, in this study, in a fractal mechanics context. Non-local interactions are modelled introducing long-range central body forces between non-adjacent volume elements of the elastic continuum. Such long-range interactions are modelled as proportional to the product of interacting volumes, to the relative displacements of the centroids and to a distance-decaying function that is monotonically-decreasing with the distance. The choice of the decaying function is a key aspect of the model and it has been proved that any continuous function, strictly positive, is thermodynamically consistent and it leads to …

A state-space approach to dynamic stability of fractional-order systems: The extended Routh-Hurwitz theorem

This paper considers the case of Beck’s column, a linear elastic cantilever column subjected to a constant follower load at its free end. The column foundation is modeled as bed of hereditary elements that react with a vertical force distributed along the beam axis. The reacting supports are modeled with spring-pot element that is a two parameters mechanical elements (C; ) with an intermediate behavior between spring and dashpot. The constitutive equation of the spring-pot involves the so called fractional order derivatives and dynamic stability problem in presence of fractional-order operator must be faced for the Beck’s column. In this study , the authors generalize Routh-Hurwitz theorem …

Molecular Dynamic Simulation on Polyamide6/Graphene nano-layers nanocomposites

In this work results obtained from Molecular Dynamic Simulation (MDS) on Polyamide 6 (PA6) chains in graphene containing nanocomposites are presented. Through detailed MDS, the interface of complex nanocomposites systems can be fully characterized, furthermore different physical properties, such as density, end-to-end distance , and average radius of gyration of polymers chains can be predicted. This issue is useful for the design of highly value-added nanocomposites and the optimization of their production process, by defining transformation steps and status variables (temperature, time and pressure), that can also help the industrial production.

How preconditioning and pretensioning of grafts used in ACLigaments surgical reconstruction are influenced by their mechanical time-dependent characteristics: Can we optimize their initial loading state?

Abstract Purpose Consensus about a pre-implant preparation protocol adaptable to any graft used in Anterior Cruciate Ligament reconstruction is still lacking. In fact, there is not agreement on reliable metrics that consider both specific graft dimensional characteristics, such as its diameter, and the inherent properties of its constitutive material, i.e. ligaments or tendons. Aim of the present study was to investigate and propose the applied engineering stress as a possible metrics. Methods Preconditioning and pretensioning protocol involved groups of grafts with different section (10 or 32 mm2) and materials (i.e. human patellar and hamstring tendons, and synthetic grafts). A 140 N load…

Seismically induced, non-stationary hydrodynamic pressure in a dam-reservoir system

Stochastic seismic analysis of hydrodynamic pressure in a dam-reservoir system is presented in this paper. The analysis is conducted assuming infinite reservoir compressible fluid and modeling seismic acceleration as a normal zero-mean stochastic process obtained by Penzien filter. The non-homogeneous boundary conditions associated to the problem have been incorporated into the equation of pressure wave scattering in the form of a forcing function turning the non-homogeneous boundary value problem into an homogeneous one. Solution obtained via modal analysis in time-domain is coupled with the use of classical Ito stochastic differential calculus to characterize the stochastic hydrodynamic p…

Hereditariness of Aortic Tissue: In-Vitro Time-Dependent Failure of Human and Porcine Specimens

This study aims to investigate the time dependent failure of aortic tissues for pathological and healthy samples by biomechanical testing. The experimental campaign has involved human pathological tissue and healthy swine tissue as preliminary study towards the development of novel failure criteria.

Non-local finite element method for the analysis of elastic continuum with long-range central interactions.

In this paper the Finite Element Method (FEM) for the mechanically-based non-local elastic continuum model is proposed. In such a model non-adjacent elements are considered mutually interacting by means of central body forces that are monotonically decreasing with their interdistance and proportional to the product of the interacting volume elements. The resulting governing equation is an integro-differential one and for such a model both kinematical and mechanical boundary conditions are exactly coincident with the classical boundary conditions of the continuum mechanics. The solution of the integro-differential problem is framed in the paper by the finite element method. Finally, the solu…

Long-range cohesive interactions of non-local continuum faced by fractional calculus

Abstract A non-local continuum model including long-range forces between non-adjacent volume elements has been studied in this paper. The proposed continuum model has been obtained as limit case of two fully equivalent mechanical models: (i) A volume element model including contact forces between adjacent volumes as well as long-range interactions, distance decaying, between non-adjacent elements. (ii) A discrete point-spring model with local springs between adjacent points and non-local springs with distance-decaying stiffness connecting non-adjacent points. Under the assumption of fractional distance-decaying interactions between non-adjacent elements a fractional differential equation in…

Fractional mechanical model for the dynamics of non-local continuum

In this chapter, fractional calculus has been used to account for long-range interactions between material particles. Cohesive forces have been assumed decaying with inverse power law of the absolute distance that yields, as limiting case, an ordinary, fractional differential equation. It is shown that the proposed mathematical formulation is related to a discrete, point-spring model that includes non-local interactions by non-adjacent particles with linear springs with distance-decaying stiffness. Boundary conditions associated to the model coalesce with the well-known kinematic and static constraints and they do not run into divergent behavior. Dynamic analysis has been conducted and both…

A non-local model of fractional heat conduction in rigid bodies

In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent s…

Non-local stiffness and damping models for shear-deformable beams

This paper presents the dynamics of a non-local Timoshenko beam. The key assumption involves modeling non-local effects as long-range volume forces and moments mutually exerted by non-adjacent beam segments, that contribute to the equilibrium of any beam segment along with the classical local stress resultants. Elastic and viscous long-range volume forces/moments are endowed in the model. They are built as linearly depending on the product of the volumes of the interacting beam segments and on generalized measures of their relative motion, based on the pure deformation modes of the beam. Attenuation functions governing the space decay of the non-local effects are introduced. Numerical resul…

Non-Local Thermoelasticity: The Fractional Heat conduction

Non-linear systems under parametric a-stable Levý white noises

Stochastic differential calculus for wind-exposed structures with autoregressive continuous (ARC) filters

In this paper, an alternative method to represent Gaussian stationary processes describing wind velocity fluctuations is introduced. The technique may be considered the extension to a time continuous description of the well-known discrete-time autoregressive model to generate Gaussian processes. Digital simulation of Gaussian random processes with assigned auto-correlation function is provided by means of a stochastic differential equation with time delayed terms forced by Gaussian white noise. Solution of the differential equation is a specific sample of the target Gaussian wind process, and in this paper it describes a digitally obtained record of the wind turbolence. The representation o…

A Fractional Approach to Non-Newtonian Blood Rheology in Capillary Vessels

In small arterial vessels, fluid mechanics involving linear viscous fluid does not reproduce experimental results that correspond to non-parabolic profiles of velocity across the vessel diameter. In this paper, an alternative approach is pursued introducing long-range interactions that describe the interactions of non-adjacent fluid volume elements due to the presence of red blood cells and other dispersed cells in plasma. These non-local forces are defined as linearly dependent on the product of the volumes of the considered elements and on their relative velocity. Moreover, as the distance between two volume elements increases, the non-local forces decay with a material distance-decaying …

FRACTIONAL-ORDER GENERALIZATION OF TRANSPORT EQUATIONS IN FRACTAL POROUS MEDIA

Random Vibrations of Uncertain Linearly Elastic Trusses

Stochastic dynamics of linear elastic trusses in presence of structural uncertainties (virtual distortion approach)

Structures involving uncertainties in material and/or in geometrical parameters are referred to as uncertain structures. Reliability analysis of such structures strongly depends on variation of parameters and probabilistic approach is often used to characterize structural uncertainties. In this paper dynamic analysis of linearly elastic system in presence of random parameter variations will be performed. In detail parameter fluctuations have been considered as inelastic, stress and parameter dependent superimposed strains. Analysis is then carried out via superposition principle accounting for response to external agencies and parameter dependent strains. Proposed method yields asymptotic s…

Experimental Characterization of the Human Meniscal Tissue

The meniscus plays a critical role in load transmission, stability and energy dissipation in the knee joint. Loss of the meniscus leads to joint degeneration and osteoarthritis. In a number of cases replacement of the resected meniscal tissue by a synthetic implant might avoid the articular cartilage degeneration. None of the available implants presents optimal biomechanics characteristic due to the fact the biomechanics functionality of the meniscus is not yet fully understood. Mimicking the native biomechanical characteristics of the menisci seems to be the key factor in meniscus replacement functioning. This is extremely challenging due to its complex inhomogeneous microstructure, the la…

Elastic waves propagation in 1D fractional non-local continuum

Aim of this paper is the study of waves propagation in a fractional, non-local 1D elastic continuum. The non-local effects are modeled introducing long-range central body interactions applied to the centroids of the infinitesimal volume elements of the continuum. These non-local interactions are proportional to a proper attenuation function and to the relative displacements between non-adjacent elements. It is shown that, assuming a power-law attenuation function, the governing equation of the elastic waves in the unbounded domain, is ruled by a Marchaud-type fractional differential equation. Wave propagation in bounded domain instead involves only the integral part of the Marchaud fraction…

Multifibrillar bundles of a self-assembling hyaluronic acid derivative obtained through a microfluidic technique for aortic smooth muscle cell orientation and differentiation

A hyaluronic acid derivative that is able to physically crosslink in a saline aqueous environment was employed for the production of fibers with a mean diameter of 50 μm using a microfluidic technique. The microfibers were collected in a tailored rotating collector and assembled to form multifibrillar bundles. The orientation of the microfibers on the collected bundles was evaluated by microCT analysis. The bundles were biofunctionalized by physical addition of fibronectin or chemical tethering of a cyRGDC peptide to achieve control of Aortic Smooth Muscle Cell (AoSMC) attachment, elongation and alignment. The mechanical performances of these bundles were evaluated by elongation tests, rela…

MECHANICAL RESPONSE OF BERNULLI EULER BEAMS ON FRACTIONAL ORDER ELASTIC FOUNDATION

The Saint-Venant cylinder under shear forces: Harmonic polynomial solution

One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis

The analysis of one-dimensional non-local elastic solids with uncertain Young's modulus is addressed. Non-local effects are represented as long-range central body forces between non-adjacent volume elements. For comparison purpose, the fluctuating elastic modulus of the material is modeled following both a probabilistic and a non-probabilistic approach. To this aim, a novel definition of the interval field concept, able to limit the overestimation affecting ordinary interval analysis, is introduced. Approximate closed-form expressions are derived for the bounds of the interval displacement field as well as for the mean-value and variance of the stochastic response.

A fractional-order model of ultra-high molecular weight polyethylene for biomedical implantation

A Non-Local Mode-I Cohesive Model for Ascending Thoracic Aorta Dissections (ATAD)

This paper presents a non-local interface mechanical model to describe aortic dissection. In this regard, the mode-I debonding problem based on a cohesive zone modeling is endowed with non-local terms to include long-range interactions that are present in multi-layered biological tissue. Such non-local effects are related to the collagen fibers that transmit forces between non-adjacent elements. Numerical simulations are provided with different values of the non-local parameters in order to show the effect of the non-locality during the debonding processes.

Ito calculus extended to non-linear systems under alpha-stable Lévy white noise

An exact thermodynamical model of power-law temperature time scaling

In this paper a physical model for the anomalous temperature time evolution (decay) observed in complex thermodynamical system in presence of uniform heat source is provided. Measures involving temperatures T with power-law variation in time as T(t)∝tβ with β∈R shows a different evolution of the temperature time rate T(t) with respect to the temperature time-dependence T(t). Indeed the temperature evolution is a power-law increasing function whereas the temperature time rate is a power-law decreasing function of time. Such a behavior may be captured by a physical model that allows for a fast thermal energy diffusion close to the insulated location but must offer more resistance to the therm…

ANALISI SPERIMENTALE DEL COMPORTAMENTO MECCANICO DI BIO-COMPOSITI RINFORZATI CON FIBRE DI AGAVE

This work deals with the study of the mechanical performance of bio-composites obtained by reinforcing both "green" thermoplastic and thermosetting matrices with natural fibers obtained by means of proper extraction processes, from two variety of agave (striata and americana) that grows in the Sicilianterritory. Through systematic experimental analyses, the mechanical performance of short fiber composites with thermoplastic matrix (PLA) obtained by hot molding, as well as composites with thermosetting matrix (tri-components "green" epoxy) obtained by hand lay-up, has been studied. Also, an innovative fiber extraction process having a zero environmental impact, have been proposed. Moreover, …

Probabilistic analysis of truss structures with uncertain parameters (virtual distortion method approach)

A new approach for probabilistic characterization of linear elastic redundant trusses with uncertainty on the various members subjected to deterministic loads acting on the nodes of the structure is presented. The method is based on the simple observation that variations of structural parameters are equivalent to superimposed strains on a reference structure depending on the axial forces on the elastic modulus of the original structure as well as on the uncertainty (virtual distortion method approach). Superposition principle may be applied to separate contribution to mechanical response due to external loads and parameter variations. Statically determinate trusses dealt with the proposed m…

Power-Laws hereditariness of biomimetic ceramics for cranioplasty neurosurgery

Abstract We discuss the hereditary behavior of hydroxyapatite-based composites used for cranioplasty surgery in the context of material isotropy. We classify mixtures of collagen and hydroxiapatite composites as biomimetic ceramic composites with hereditary properties modeled by fractional-order calculus. We assume isotropy of the biomimetic ceramic is assumed and provide thermodynamic of restrictions for the material parameters. We exploit the proposed formulation of the fractional-order isotropic hereditariness further by means of a novel mechanical hierarchy corresponding exactly to the three-dimensional fractional-order constitutive model introduced.

Convergence of Boobnov-Galerkin Method Exemplified

In this Note, Boobnov–Galerkin’s method is proved to converge to an exact solution for an applied mechanics problem. We address in detail the interrelation of Boobnov–Galerkin method and the exact solution in the beam deflection problems. Namely, we show the coincidence of these two methods for clamped–clamped boundary conditions, using an alternative set of functions proposed by Filonenko-Borodich.12 Received 25 February 2003; accepted for publication 13 March 2004. Copyright c 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to th…

Identification of circumferential regional heterogeneity of ascending thoracic aneurysmal aorta by biaxial mechanical testing

Abstract Ascending thoracic aortic aneurysm (ATAA) in patients with bicuspid aortic valve (BAV) can present an asymmetrical aortic dilatation compared with patients with tricuspid aortic valve (TAV). This pattern of aneurysm dilatation led us to hypothesize that biomechanical differences likely induced by regional heterogeneity of material properties can underlie the observed asymmetric enlargement discrepancies between BAV ATAA and TAV ATAA. This study aimed to characterize the mechanical properties and associated aortic tissue stiffness changes along the circumferential direction of aortic rings collected from surgically-repaired patients with ATAA. Biaxial material testing was performed …

A physical description of fractional-order Fourier diffusion

In this paper the authors introduce a physical picture of anomalous heat transfer in rigid conductor. The analysis shows that a fractional-order Fourier transport is obtained by the analysis of the heat transport in a functionally graded conductor. The order of the fractional-type operator obtained is related to the grading of the physical properties of the conductor.

Fractional differential calculus for 3D mechanically based non-local elasticity

This paper aims to formulate the three-dimensional (3D) problem of non-local elasticity in terms of fractional differential operators. The non-local continuum is framed in the context of the mechanically based non-local elasticity established by the authors in a previous study; Non-local interactions are expressed in terms of central body forces depending on the relative displacement between non-adjacent volume elements as well as on the product of interacting volumes. The non-local, long-range interactions are assumed to be proportional to a power-law decaying function of the interaction distance. It is shown that, as far as an unbounded domain is considered, the elastic equilibrium proble…

Long-range interactions in 1D heterogeneous solids with uncertainty

Abstract In this paper, the authors aim to analyze the response of a one-dimensional non-local elastic solid with uncertain Young's modulus. The non-local effects are represented as long-range central body forces between non-adjacent volume elements. Following a non-probabilistic approach, the fluctuating elastic modulus of the material is modeled as an interval field. The analysis is conducted resorting to a novel formulation that confines the overestimation effect involved in interval models. Approximate closed-form expressions are derived for the bounds of the interval displacement field.

An explicit mechanical interpretation of Eringen non-local elasticity by means of fractional calculus

If the attenuation function of strain is expressed as a power law, the formalism of fractional calculus may be used to handle Eringen non-local elastic model. Aim of the present paper is to provide a mechanical interpretation to this non-local fractional elastic model by showing that it is equivalent to a discrete, point-spring model. A one-dimensional geometry is considered; static, kinematic and constitutive equations as well as the proper boundary conditions are derived and discussed.

Finite element method for a nonlocal Timoshenko beam model

A finite element method is presented for a nonlocal Timoshenko beam model recently proposed by the authors. The model relies on the key idea that nonlocal effects consist of long-range volume forces and moments exchanged by non-adjacent beam segments, which contribute to the equilibrium of a beam segment along with the classical local stress resultants. The long-range volume forces/moments are linearly depending on the product of the volumes of the interacting beam segments, and their relative motion measured in terms of the pure beam deformation modes, through appropriate attenuation functions governing the spatial decay of nonlocal effects. In this paper, the beam model is reformulated wi…

Fractional hereditariness of lipid membranes: Instabilities and linearized evolution

In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elas- ticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is studied by minimizing the Gibbs free energy which penalizes perturbations of the changes of areal stretch and their gradients only [1]. As material instabilities arise whenever areal stretches characterizing homogeneous configurations lie inside the spinoidal zone of the free energy density, bifurcations from such configurations are shown to occur as oscillatory perturbations of the in-plane displacement. Experimental observations [2] show a power-law in-pl…

The finite element method for the mechanically-based model of non-local continuum

In this paper the finite element method (FEM) for the mechanically based non-local elastic continuum model is proposed. In such a model each volume element of the domain is considered mutually interacting with the others, beside classical interactions involved by the Cauchy stress field, by means of central body forces that are monotonically decreasing with their inter-distance and proportional to the product of the interacting volume elements. The constitutive relations of the long-range interactions involve the product of the relative displacement of the centroids of volume elements by a proper, distance-decaying function, which accounts for the decrement of the long-range interactions as…

Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory

In this paper the physically-based approach to non-local elasticity theory is introduced. It is formulated by reverting the continuum to an ensemble of interacting volume elements. Interactions between adjacent elements are classical contact forces while long-range interactions between non-adjacent elements are modelled as distance-decaying central body forces. The latter are proportional to the relative displacements rather than to the strain field as in the Eringen model and subsequent developments. At the limit the displacement field is found to be governed by an integro-differential equation, solved by a simple discretization procedure suggested by the underlying mechanical model itself…

Toward high performance renewable agave reinforced biocomposites: Optimization of fiber performance and fiber-matrix adhesion analysis

Abstract The increasing sensitivity toward the environmental pollution and the recent laws on the environmental protection, have led to an increasing attention to the so called biocomposites, i.e. to ecofriendly or renewable composite materials, obtained from biopolymers reinforced by natural fibers. Although the contribution of various works reported in literature, focused on biocomposites reinforced by agave fibers, such materials are still exclusively used in the automotive industry for non-structural applications, and the implementation of high performance biocomposites for semi-structural and structural applications, is an expected, but not yet reached objective. Therefore, the present…

Patient-specific computational evaluation of stiffness distribution in ascending thoracic aortic aneurysm

Quantifying local aortic stiffness properties in vivo is acknowledged as essential to assess the severity of an ascending thoracic aortic aneurysm (ATAA). Recently, the LESI (local extensional stiffness identification) methodology has been established to quantify non-invasively local stiffness properties of ATAAs using electrocardiographic-gated computed tomography (ECG-gated CT) scans. The aim of the current study was to determine the most sensitive markers of local ATAA stiffness estimation with the hypothesis that direct measures of local ATAA stiffness could better detect the high-risk patients. A cohort of 30 patients (12 BAV and 18 TAV) referred for aortic size evaluation by ECG-gated…

A numerical assessment of the free energy function for fractional-order relaxation

In this paper a novel method based on complex eigenanalysis in the state variables domain is proposed to uncouple the set of rational order fractional differential equations governing the dynamics of multi-degree-of-freedom system. The traditional complex eigenanalysis is appropriately modified to be applicable to the coupled fractional differential equations. This is done by expanding the dimension of the problem and solving the system in the state variable domain. Examples of applications are given pertaining to multi-degree-of-freedom systems under both deterministic and stochastic loads.

Can biomechanical analysis shed some light on aneurysmal pathophysiology? Preliminary study on ex vivo cerebral arterial walls

Abstract Background The pathophysiology of cerebral aneurysm is complex and poorly understood, and it can have the most catastrophic clinical presentation. Flow dynamics is a key player in the initiation and progression of aneurysm. Better understanding the interaction between hemodynamic loading and biomechanical wall responses can help to add the missing piece on aneurysmal pathophysiology. In this laboratory study we aimed to analyze the effect of the application of a mechanical force to cerebral arterial walls. Methods Displacement control tests were performed on five porcine cerebral arteries. The test machine was the T150 Nanotensile. The stiffness variation with the increment of the …

Fractional differential equations and related exact mechanical models

Creep and relaxation tests, performed on various materials like polymers, rubbers and so on are well-fitted by power-laws with exponent β ∈ [0, 1] (Nutting (1921), Di Paola et al. (2011)). The consequence of this observation is that the stress-strain relation of hereditary materials is ruled by fractional operators (Scott Blair (1947), Slonimsky (1961)). A large amount of researches have been performed in the second part of the last century with the aim to connect constitutive fractional relations with some mechanical models by means of fractance trees and ladders (see Podlubny (1999)). Recently, Di Paola and Zingales (2012) proposed a mechanical model that corresponds to fractional stress-…

Fractional-Order Theory of Thermoelasticity. II: Quasi-Static Behavior of Bars

This work aims to shed light on the thermally-anomalous coupled behavior of slightly deformable bodies, in which the strain is additively decomposed in an elastic contribution and in a thermal part. The macroscopic heat flux turns out to depend upon the time history of the corresponding temperature gradient, and this is the result of a multiscale rheological model developed in Part I of the present study, thereby resembling a long-tail memory behavior governed by a Caputo's fractional operator. The macroscopic constitutive equation between the heat flux and the time history of the temperature gradient does involve a power law kernel, resulting in the anomaly mentioned previously. The interp…

A fractional-order model for aging materials: An application to concrete

Abstract In this paper, the hereditariness of aging materials is modeled within the framework of fractional calculus of variable order. A relevant application is made for the long-term behavior of concrete, for which the creep function is evaluated with the aid of Model B3. The corresponding relaxation function is derived through the Volterra iterated kernels and a comparison with the numerically-obtained relaxation function of Model B3 is also reported. The proposed fractional hereditary aging model (FHAM) for concretes leads to a relaxation function that fully agrees with the well-established Model B3. Furthermore, the FHAM takes full advantage of the formalism of fractional-order calculu…

Mechanically-based approach to non-local elasticity: Variational principles

Abstract The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Mo…

Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee

In this paper the authors introduce a nonlinear model of fractional-order hereditariness used to capture experimental data obtained on human tendons of the knee. Creep and relaxation data on fibrous tissues have been obtained and fitted with logarithmic relations that correspond to power-laws with nonlinear dependence of the coefficients. The use of a proper nonlinear transform allows one to use Boltzmann superposition in the transformed variables yielding a fractional-order model for the nonlinear material hereditariness. The fundamental relations among the nonlinear creep and relaxation functions have been established, and the results from the equivalence relations have been contrasted wi…

A discrete mechanical model of fractional hereditary materials

Fractional hereditary materials are characterized for the presence, in the stress-strain relations, of fractional-order operators with order beta a[0,1]. In Di Paola and Zingales (J. Rheol. 56(5):983-1004, 2012) exact mechanical models of such materials have been extensively discussed obtaining two intervals for beta: (i) Elasto-Viscous (EV) materials for 0a parts per thousand currency sign beta a parts per thousand currency sign1/2; (ii) Visco-Elastic (VE) materials for 1/2a parts per thousand currency sign beta a parts per thousand currency sign1. These two ranges correspond to different continuous mechanical models. In this paper a discretization scheme based upon the continuous models p…

On the vibrations of a mechanically based non-local beam model

The vibration problem of a Timoshenko non-local beam is addressed. The beam model involves assuming that the equilibrium of each volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are taken as depending on the product of the interacting volume elements and on their relative displacement through a material-dependent distance-decaying function. To derive the motion equations and the related mechanical boundary conditions, the Hamilton's principle is applied The vibration problem of a Timoshenko non-local beam …

On the role of material properties in ascending thoracic aortic aneurysms

One of the obstacles standing before the biomechanical analysis of an ascending thoracic aortic aneurysm (ATAA) is the difficulty in obtaining patient-specific material properties. This study aimed to evaluate differences on ATAA-related stress predictions resulting from the elastostatic analysis based on the optimization of arbitrary material properties versus the application of patient-specific material properties determined from ex-vivo biaxial testing. Specifically, the elastostatic analysis relies the on the fact that, if the aortic wall stress does not depend on material properties, the aorta has to be statistically determinate. Finite element analysis (FEA) was applied to a group of …

Finite-Element Formulation of a Nonlocal Hereditary Fractional-Order Timoshenko Beam

AbstractA mechanically-based nonlocal Timoshenko beam model, recently proposed by the authors, hinges on the assumption that nonlocal effects can be modeled as elastic long-range volume forces and moments mutually exerted by nonadjacent beam segments, which contribute to the equilibrium of any beam segment along with the classical local stress resultants. Long-range volume forces/moments linearly depend on the product of the volumes of the interacting beam segments, and on pure deformation modes of the beam, through attenuation functions governing the space decay of nonlocal effects. This paper investigates the response of this nonlocal beam model when viscoelastic long-range interactions a…

Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEM) of a Customized Stent-Graft for Endovascular (EVAR) Treatment of Abdominal Aortic Aneurism (AAA)

Background: The treatment of abdominal aortic aneurysm (AAA) is today commonly treated by inserting a stent-graft by the endovascular route, without resorting to open surgery. However, some clinical cases do not allow this less invasive approach, meaning that the stent-graft cannot be inserted and open surgery is used. Methods: In the study, we propose a fluid–structure interaction (FSI) analysis of an aneurysmatic aorta that could not be treated with Endovascular Aneurysm Repair (EVAR). The vessel is reconstructed through segmentation from CT scans and subsequently modeled on CAD software to create the surface and thickness of the vessel itself. Subsequently, we proceeded to carry out Comp…

Towards Mechanical Modelling for Fractional Hereditariness of Lipid Membranes

A fractional order theory of poroelasticity

Abstract We introduce a time memory formalism in the flux-pressure constitutive relation, ruling the fluid diffusion phenomenon occurring in several classes of porous media. The resulting flux-pressure law is adopted into the Biot’s formulation of the poroelasticity problem. The time memory formalism, useful to capture non-Darcy behavior, is modeled by the Caputo’s fractional derivative. We show that the time-evolution of both the degree of settlement and the pressure field is strongly influenced by the order of Caputo’s fractional derivative. Also a numerical experiment aiming at simulating the confined compression test poroelasticity problem of a sand sample is performed. In such a case, …

STRUMENTO MEDICO PER INSERIMENTI INTRALUMINALI

La presente invenzione trova applicazione nel settore dei dispositivi medici inseribili all’interno del corpo umano ed ha particolarmente per oggetto uno strumento medico per inserimenti intraluminali, quali dispositivi per incannulazione o cateterizzazione del sistema vascolare.

Modellazione e risposta di strutture continue a parametri incerti mediante processi Poissoniani filtrati

A numerical integration approach for fractional‐order viscoelastic analysis of hereditary‐aging structures

Fractional-order theory of thermoelasticicty. I: Generalization of the Fourier equation

The paper deals with the generalization of Fourier-type relations in the context of fractional-order calculus. The instantaneous temperature-flux equation of the Fourier-type diffusion is generalized, introducing a self-similar, fractal-type mass clustering at the micro scale. In this setting, the resulting conduction equation at the macro scale yields a Caputo's fractional derivative with order [0,1] of temperature gradient that generalizes the Fourier conduction equation. The order of the fractional-derivative has been related to the fractal assembly of the microstructure and some preliminary observations about the thermodynamical restrictions of the coefficients and the state functions r…

A new displacement-based framework for non-local Timoshenko beams

In this paper, a new theoretical framework is presented for modeling non-locality in shear deformable beams. The driving idea is to represent non-local effects as long-range volume forces and moments, exchanged by non-adjacent beam segments as a result of their relative motion described in terms of pure deformation modes of the beam. The use of these generalized measures of relative motion allows constructing an equivalent mechanical model of non-local effects. Specifically, long-range volume forces and moments are associated with three spring-like connections acting in parallel between couples of non-adjacent beam segments, and separately accounting for pure axial, pure bending and pure sh…

Power-law hereditariness of hierarchical fractal bones

In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ≤ β ≤1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the e…

Free energy and states of fractional-order hereditariness

AbstractComplex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.

Probabilistic Analysis of Non-Local 1-D Continuum under Random Load

A mechanically based approach to non-local beam theories

A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, t…

Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness

Non-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linear model of the springpot is defined in terms of a single integral with separable kernel endowed with a non-linear transform of the state variable that allows for the use of Boltzmann superposition. The model represents a self-similar hierarchy that allows for a time-invariance as the result of the application of the conservation laws at any resolution scale. It is shown that the non-linear spring…

A Non-Local Two Dimensional Foundation Model

Classical foundation models such as the Pasternak and the Reissner models have been recently reformulated within the framework of non-local mechanics, by using the gradient theory of elasticity. To contribute to the research effort in this field, this paper presents a two-dimensional foundation model built by using a mechanically based non-local elasticity theory, recently proposed by the authors. The foundation is thought of as an ensemble of soil column elements resting on an elastic base. It is assumed that each column element is acted upon by a local Winkler-like reaction force exerted by the elastic base, by contact shear forces and volume forces due, respectively, to adjacent and non-…

The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions

Abstract This paper presents the generalization to a three-dimensional (3D) case of a mechanically-based approach to non-local elasticity theory, recently proposed by the authors in a one-dimensional (1D) case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range forces exerted by non-adjacent elements. Specifically, the long-range forces are modelled as central body forces depending on the relative displacement between the centroids of the volume elements, measured along the line connecting the centroids. Further, the long-range forces are assumed to be proportional to a proper, material-dependent, dis…

Cardiovascular parameters detection using a Photoplethismographic system

We propose an innovative, cost-effective and easy to employ photoplethysmographic (PPG) system using Silicon Photomultipliers (SiPMs) sensors to measure cardiovascular parameters that can potentially represent markers for arterial stiffness

Stochastic seismic analysis of hydrodynamic pressure in dam reservoir systems

Hydrodynamic seismic-induced pressure requires careful consideration in the aseismic design of dams. Effects induced by earthquake excitation may cause many-fold increments of hydrostatic pressure. In this study earthquake excitation has been modelled by means of random process theory obtaining the response statistics of a dam-reservoir dynamical system. The analysis has been conducted assuming a rigid retaining wall of the reservoir and dissipative fluid. Copyright © 2002 John Wiley & Sons, Ltd.

Power-law hereditariness of hierarchical fractal bones

SUMMARY In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann–Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related …

The mechanically based non-local elasticity: an overview of main results and future challenges

The mechanically based non-local elasticity has been used, recently, in wider and wider engineering applications involving small-size devices and/or materials with marked microstructures. The key feature of the model involves the presence of non-local effects as additional body forces acting on material masses and depending on their relative displacements. An overview of the main results of the theory is reported in this paper.

Multi-objective optimization of nitinol stent design.

Nitinol stents continuously experience loadings due to pulsatile pressure, thus a given stent design should possess an adequate fatigue strength and, at the same time, it should guarantee a sufficient vessel scaffolding. The present study proposes an optimization framework aiming at increasing the fatigue life reducing the maximum strut strain along the structure through a local modification of the strut profile.The adopted computational framework relies on nonlinear structural finite element analysis combined with a Multi Objective Genetic Algorithm, based on Kriging response surfaces. In particular, such an approach is used to investigate the design optimization of planar stent cell.The r…

Materials Science Forum

This paper deals with the generalization to three-dimensional elasticity of the physically-based approach to non-local mechanics, recently proposed by the authors in one-dimensional case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range central forces exerted by non-adjacent elements. Specifically, the long-range forces are modeled as central body forces depending on the relative displacements between the centroids of the volume elements, measured along the line connecting the centroids. Furthermore, the long-range forces are assumed to be proportional to a proper, material-dependent, distance-decay…

Mechanically Based Nonlocal Euler-Bernoulli Beam Model

AbstractThis paper presents a nonlocal Euler-Bernoulli beam model. It is assumed that the equilibrium of a beam segment is attained because of the classical local stress resultants, along with long-range volume forces and moments exchanged by the beam segment with all the nonadjacent beam segments. Elastic long-range volume forces/moments are considered, built as linearly depending on the product of the volumes of the interacting beam segments and on generalized measures of their relative motion, based on the pure deformation modes of the beam. Attenuation functions governing the space decay of the nonlocal effects are introduced. The motion equations are derived in an integro-differential …

Probabilistic analysis of uncertain Bernoulli-Euler beams

Numerical Simulations of the Hydrodynamics of the Abdominal Aorta Aneurysm (AAA) Using a Smoothed Particle Hydrodynamics Code with Deformable Wall Preliminary Results

We present some preliminary results of the numerical simulations of the hydrodynamic characteristics of an abdominal aorta aneurysm (AAA) patient specific test case. Images of the AAA lumen have been acquired in 10 discrete time-steps through a stabilized cardiac cycle by electrocardiogram-gated computer tomography angiography, and are used to approximate the in vivo, time dependent kinematic fields of the (internal) arterial wall. The flow field is simulated by a Smoothed Particle SPH numerical model, where the kinematics of the boundary of the computational domain (the internal aortic vessel) is the one computed by the above procedure. The outputs of the SPH model, i.e., pressure and flow…

Itô calculus extended to systems driven by -stable Lévy white noises (a novel clip on the tails of Lévy motion)

Abstract The paper deals with probabilistic characterization of the response of non-linear systems under α -stable Levy white noise input. It is shown that, by properly selecting a clip in the probability density function of the input, the moments of the increments of Levy motion process remain all of the same order ( d t ) , like the increments of the Compound Poisson process. It follows that the Ito calculus extended to Poissonian input, may also be used for α -stable Levy white noise input processes. It is also shown that, when the clip on the tails of the probability of the increments of the Levy motion approaches to infinity, the Einstein–Smoluchowsky equation is restored. Once these c…

Enhanced In Situ Availability of Aphanizomenon Flos-Aquae Constituents Entrapped in Buccal Films for the Treatment of Oxidative Stress-Related Oral Diseases: Biomechanical Characterization and In Vitro/Ex Vivo Evaluation

In recent years, the key role of oxidative stress in pathogenesis of oral diseases has been emphasized and the use of antioxidant agents has been encouraged. Aphanizomenon flos-aquae (AFA) is a unicellular blue-green alga with antioxidant and anti-inflammatory properties. The aim of this study was the formulation and characterization of mucoadhesive thin layer films loaded with AFA, finalized to the treatment of oxidative stress (OS)-related oral diseases. First, to enhance the bioavailability of AFA constituents, the raw food grade material was appropriately treated by a high frequency homogenization able to disrupt cell walls. Thus, Eudragit&reg

Biopolyester-based systems containing naturally occurring compounds suitable for biomedical devices

A Viscoelastic Model for the Long-Term Deflection of Segmental Prestressed Box Girders

Most of segmental prestressed concrete box girders exhibit excessive multidecade deflections unforeseeable by past and current design codes. To investigate such a behavior, mainly caused by creep and shrinkage phenomena, an effective finite element (FE) formulation is presented in this article. This formulation is developed by invoking the stationarity of an energetic principle for linear viscoelastic problems and relies on the Bazant creep constitutive law. A case study representative of segmental prestressed concrete box girders susceptible to creep is also analyzed in the article, that is, the Colle Isarco viaduct. Its FE model, based on the aforementioned energetic formulation, was succ…

Fractional-order constitutive equations in mechanics and thermodynamics

This chapter is devoted to the application of fractional calculus in mechanics of materials and thermodynamics. The use of fractional calculus in mechanics is related to the definition of fractional-order constitutive equations leading to the class of fractional hereditariness. In this regard, a brief description of the classical rheological models of material hereditariness and a comparison with the fractional elements are reported. It is shown that a rheological hierarchy corresponding to the fractional order stress-strain relation may be defined. Such a model provides a multi-scale mechanical picture of the power-law hereditariness and it leads toward an unique definition of material fre…

A Wavelet-Galerkin Method for a 1D Elastic Continuum with Long- Range Interactions

An elastic continuum model with long-range forces is addressed in this study. The model stems from a physically-based approach to non-local mechanics where non-adjacent volume elements exchange mutual central forces that depend on the relative displacement and on the product between the interacting volume elements; further, they are taken as proportional to a material dependent and distance-decaying function. Smooth-decay functions lead to integrodifferential equations while hypersingular, fractional-decay functions lead to a fractional differential equation of Marchaud type. In both cases the governing equations are solved by the Galerkin method with different sets of basis functions, amon…

The finite element method for fractional non-local thermal energy transfer in non-homogeneous rigid conductors

Abstract In a non-local fractional-order model of thermal energy transport recently introduced by the authors, it is assumed that local and non-local contributions coexist at a given observation scale: while the first is described by the classical Fourier transport law, the second involves couples of adjacent and non-adjacent elementary volumes, and is taken as proportional to the product of the masses of the interacting volumes and their relative temperature, through a material-dependent, distance-decaying power-law function. As a result, a fractional-order heat conduction equation is derived. This paper presents a pertinent finite element method for the solution of the proposed fractional…

Quasi-Fractional Models of Human Tendons Hereditariness

In this study, the authors, after collecting a series of experimental evidences following a creep and relaxation tendon campaign, propose a non-linear model of the viscoelastic behavior of the tendons. The ligaments investigated are the patellars and the hamstrings. The analytical model proposed by the authors aims to explain the non-linear hereditary behavior of these tissues and proposes an approach with which to develop a hereditary fractional-order non-linear model.

Probabilistic analyisis of uncertain Bernoulli-Euler beams via Virtual Distortion Method

Stochastic analysis of linear and nonlinear systems under α-stable Lèvy white noise

In Vitro Measurement of Strain Localization Preceding Dissection of the Aortic Wall Subjected to Radial Tension

AbstractBackgroundAortic dissection (AD) is a common pathology and challenging clinical problem. A better understanding of the biomechanical effects preceding its initiation is essential for predicting adverse events on a patient-specific basis. Moreover, the predictability of patient-specific biomechanics-based computational models is hampered by uncertainty about boundary conditions and material properties.ObjectivePredisposition of thoracic aortic aneurysms (TAA) to ADs can be related to the degradation of biomechanically important constituents in the aortic wall of TAAs. The goal of the present study is to develop a new methodology to measure strain fields in aortic tissues subjected to…

A fractional viscoelastic non-local Timoshenko beam

Variational Aspects of the Physically-Based Approach to 3D Non-Local Continuum Mechanics

This paper deals with the generalization to three-dimensional elasticity of the physically-based approach to non-local mechanics, recently proposed by the authors in one-dimensional case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range central forces exerted by non-adjacent elements. Specifically, the long-range forces are modeled as central body forces depending on the relative displacements between the centroids of the volume elements, measured along the line connecting the centroids. Furthermore, the long-range forces are assumed to be proportional to a proper, material-dependent, distance-decay…

A Fractional-Order Model of Biopolyester Containing Naturally Occurring Compounds for Soil Stabilization

Currently, the use of polymers and biopolymers as soil-stabilizer additives for control of the soil degradation, deterioration, and desertification and for improving the arid and semiarid soils has been expanded significantly in the agricultural sector. This research was conducted to determine the effect of naturally occurring compounds, such as quercetin (Q) and sodium montmorillonite (NaMMt) at different weight ratios, in biopolyester, such as polylactic acid (PLA), aiming to formulate ecosustainable materials to control the soil degradation and to protect the environment. As known, the use of sophisticated analytical tools to describe the material rheology and melting properties is nowad…

Il modello autoregressivo continuo (ARC) per l'analisi dinamica di strutture esposte al vento

Development and characterization of xyloglucan-poly(vinyl alcohol) hydrogel membrane for wireless smart wound dressings

Research which addresses advanced wound management can contribute to the needs of modern healthcare, especially in situations that require continuous monitoring, analysis, responsive therapeutic treatments and data recording. The development of “smart” bandages and dressings that can remotely monitor relevant parameters for the wound healing process without a hospital intervention can be very useful tools for patients and physicians and for advancing the understanding of the healing process. In the present work, biocompatible xyloglucan/poly(vinyl alcohol) hydrogels are being developed as smart wound dressings that, in addition to the traditional favorable properties of hydrogels as skin ca…

Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise

In this study stochastic analysis of non-linear dynamical systems under α-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function …

Fractional calculus in solid mechanics: local versus non-local approach

Several enriched continuum mechanics theories have been proposed by the scientific community in order to develop models capable of describing microstructural effects. The aim of the present paper is to revisit and compare two of these models, whose common denominator is the use of fractional calculus operators. The former was proposed to investigate damage in materials exhibiting a fractal-like microstructure. It makes use of the local fractional derivative, which turns out to be a powerful tool to describe irregular patterns such as strain localization in heterogeneous materials. On the other hand, the latter is a non-local approach that models long-range interactions between particles by …

Letter to the Editor. The missing piece to solve the equation.

Special Issue on “Frontier Biomechanical Challenges in Cardiovascular Physiopathology”

This special issue collects a number of original contributions, which were presented and discussed during the thematic Symposium organized by the Italian Chapter of the European Society of Biomechanics (ESB) in collaboration with the Mediterranean Institute for Transplantation and Advanced Specialized Therapies (ISMETT – IRCCS), the Fondazione RiMED and the University of Palermo. The Symposium focused on recent advances in cardiovascular biomechanics, and the promise they hold for clinical therapeutic strategies and future research.

Il Filtro Integrale Auto-Regressivo Continuo (I-ARC) per l’Analisi di Strutture Esposte al Vento

In questo studio viene proposto un metodo per la rappresentazione di processi aleatori Gaussiani e stazionari, utile a modellare la turbolenza della velocità del vento, introducendo la versione integrale del modello auto-regressivo discreto già proposto in precedenza. La rappresentazione di un processo aleatorio di assegnata funzione di correlazione viene condotta integrando un’equazione integro-differenziale in cui viene coinvolto un nucleo, che rappresenta la memoria del processo, in presenza di un rumore bianco Gaussiano. La soluzione dell’equazione rappresenta un campione del processo aleatorio della turbolenza della velocità del vento. E’ stato mostrato che il modello I-ARC fornisce, n…