Solutions for the Design and Increasing of Efficiency of Viscous Dampers

In last decades many strategies for seismic vulnerability mitigation of structures have been studied and experimented; in particular energy dissipation by external devices assumes a great importance for the relative simplicity and efficacy. Among all possible approaches the use of fluid viscous dampers are very interesting, because of their velocity-dependent behaviour and relatively low costs. Application on buildings requires a specific study under seismic excitation and a particular attention on structural details. Nevertheless seismic codes give only general information and in most case the design of a such protection systems results difficult; this problem is relevant also in Italy whe…

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process

Abstract In this paper, the widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main results available in literature in several decades of contributions. The most simple application of the method is related to the solution of Fokker–Planck type equations. In this paper, the solution in the presence of normal, α-stable, and Poissonian white noises is first discussed. Then, application to barrier problems, such as first passage problems and vibroimpact problems is described. Further, the extension of the path integral method to problems involving multi-degrees-of-freedom systems is anal…

Earthquake ground motion artificial simulations through Fractional Tajimi-Kanai Model

On the dynamics of non-local fractional viscoelastic beams under stochastic agencies

Abstract Non-local viscoelasticity is a subject of great interest in the context of non-local theories. In a recent study, the authors have proposed a non-local fractional beam model where non-local effects are represented as viscoelastic long-range volume forces and moments, exchanged by non-adjacent beam segments depending on their relative motion, while local effects are modelled by elastic classical stress resultants. Long-range interactions have been given a fractional constitutive law, involving the Caputo's fractional derivative. This paper introduces a comprehensive numerical approach to calculate the stochastic response of the non-local fractional beam model under Gaussian white no…

Fractional Tajimi–Kanai model for simulating earthquake ground motion

The ground acceleration is usually modeled as a filtered Gaussian process. The most common model is a Tajimi–Kanai (TK) filter that is a viscoelastic Kelvin–Voigt unit (a spring in parallel with a dashpot) carrying a mass excited by a white noise (acceleration at the bedrock). Based upon the observation that every real material exhibits a power law trend in the creep test, in this paper it is proposed the substitution of the purely viscous element in the Kelvin Voigt element with the so called springpot that is an element having an intermediate behavior between purely elastic (spring) and purely viscous (dashpot) behavior ruled by fractional operator. With this choice two main goals are rea…

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…

Complex fractional moments for the characterization of the probabilistic response of non-linear systems subjected to white noises

In this chapter the solution of Fokker-Planck-Kolmogorov type equations is pursued with the aid of Complex Fractional Moments (CFMs). These quantities are the generalization of the well-known integer-order moments and are obtained as Mellin transform of the Probability Density Function (PDF). From this point of view, the PDF can be seen as inverse Mellin transform of the CFMs, and it can be obtained through a limited number of CFMs. These CFMs’ capability allows to solve the Fokker-Planck-Kolmogorov equation governing the evolutionary PDF of non-linear systems forced by white noise with an elegant and efficient strategy. The main difference between this new approach and the other one based …

On the behavior of a three-dimensional fractional viscoelastic constitutive model

In this paper a three-dimensional isotropic fractional viscoelastic model is examined. It is shown that if different time scales for the volumetric and deviatoric components are assumed, the Poisson ratio is time varying function; in particular viscoelastic Poisson ratio may be obtained both increasing and decreasing with time. Moreover, it is shown that, from a theoretical point of view, one-dimensional fractional constitutive laws for normal stress and strain components are not correct to fit uniaxial experimental test, unless the time scale of deviatoric and volumetric are equal. Finally, the model is proved to satisfy correspondence principles also for the viscoelastic Poisson’s ratio a…

Einstein-Smoluchowsky equation handled by complex fractional moments

In this paper the response of a non linear half oscillator driven by α-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDF of such a system is ruled by the so called Einstein-Smoluchowsky equation involving, in the diffusive term, the Riesz fractional derivative. The solution is obtained by the use of complex fractional moments of the PDF, calculated with the aid of Mellin transform operator. It is shown that solution can be found for various values of stability index α and for any nonlinear function of the drift term in the stochastic differential equation.

Stochastic Analysis of a Nonlocal Fractional Viscoelastic Bar Forced by Gaussian White Noise

Recently, a displacement-based nonlocal bar model has been developed. The model is based on the assumption that nonlocal forces can be modeled as viscoelastic (VE) long-range interactions mutually exerted by nonadjacent bar segments due to their relative motion; the classical local stress resultants are also present in the model. A finite element (FE) formulation with closed-form expressions of the elastic and viscoelastic matrices has also been obtained. Specifically, Caputo's fractional derivative has been used in order to model viscoelastic long-range interaction. The static and quasi-static response has been already investigated. This work investigates the stochastic response of the non…

Viscoelastic material models for more accurate polyethylene wear estimation

Wear debris from ultra-high-molecular-weight polyethylene components used for joint replacement prostheses can cause significant clinical complications, and it is essential to be able to predict implant wear accurately in vitro to prevent unsafe implant designs continuing to clinical trials. The established method to predict wear is simulator testing, but the significant equipment costs, experimental time and equipment availability can be prohibitive. It is possible to predict implant wear using finite element methods, though those reported in the literature simplify the material behaviour of polyethylene and typically use linear or elastoplastic material models. Such models cannot represe…

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.

A Non-stationary Fractional Tajimi Kanai Model of Earthquake Ground Motions

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 …

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…

Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments

Abstract The probability density function of the response of a nonlinear system under external α -stable Levy white noise is ruled by the so called Fractional Fokker–Planck equation. In such equation the diffusive term is the Riesz fractional derivative of the probability density function of the response. The paper deals with the solution of such equation by using the complex fractional moments. The analysis is performed in terms of probability density for a linear and a non-linear half oscillator forced by Levy white noise with different stability indexes α . Numerical results are reported for a wide range of non-linearity of the mechanical system and stability index of the Levy white nois…

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.

Simplified analytical models for compressed concrete columns confined by FRP and FRCM system

In order to consider the response of concrete columns confined by FRP and FRCM system, proper models have to be formulated. In this context the present paper shows a generalized criterion for the determination of the increase in strength, in ductility and in dissipated energy for varying corner radius ratio of the cross section and fiber volumetric ratio. The procedure is based on the best fitting of several experimental data and unlike the usual empirical approaches available in the literature, the proposed technique relates the confinement effectiveness to a single parameter representative of the relative stiffness between the original concrete core and the reinforcement system. Furthermo…

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 …

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…

A Mellin transform approach to wavelet analysis

The paper proposes a fractional calculus approach to continuous wavelet analysis. Upon introducing a Mellin transform expression of the mother wavelet, it is shown that the wavelet transform of an arbitrary function f(t) can be given a fractional representation involving a suitable number of Riesz integrals of f(t), and corresponding fractional moments of the mother wavelet. This result serves as a basis for an original approach to wavelet analysis of linear systems under arbitrary excitations. In particular, using the proposed fractional representation for the wavelet transform of the excitation, it is found that the wavelet transform of the response can readily be computed by a Mellin tra…

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 …

Cross-correlation and cross-power spectral density representation by complex spectral moments

Abstract A new approach to provide a complete characterization of normal multivariate stochastic vector processes is presented in this paper. Such proposed method is based on the evaluation of the complex spectral moments of the processes. These quantities are strictly related to the Mellin transform and they are the generalization of the integer-order spectral moments introduced by Vanmarcke. The knowledge of the complex spectral moments permits to obtain the power spectral densities and their cross counterpart by a complex series expansions. Moreover, with just the aid of some mathematical properties the complex fractional moments permit to obtain also the correlation and cross-correlatio…

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…

The finite element implementation of 3D fractional viscoelastic constitutive models

Abstract The aim of this paper is to present the implementation of 3D fractional viscoelastic constitutive theory presented in Alotta et al., 2016 [1]. Fractional viscoelastic models exactly reproduce the time dependent behaviour of real viscoelastic materials which exhibit a long “fading memory”. From an implementation point of view, this feature implies storing the stress/strain history throughout the simulations which may require a large amount of memory. We propose here a number of strategies to effectively limit the memory required. The form of the constitutive equations are summarized and the finite element implementation in a Newton-Raphson integration scheme is described in detail. …

Analysis of Fractional Viscoelastic Material With Mechanical Parameters Dependent on Random Temperature

It is well known that mechanical parameters of polymeric materials, e.g., epoxy resin, are strongly influenced by the temperature. On the other hand, in many applications, the temperature is not known exactly during the design process and this introduces uncertainties in the prevision of the behavior also when the stresses are deterministic. For this reason, in this paper, the mechanical behavior of an epoxy resin is characterized by means of a fractional viscoelastic model at different temperatures; then, a simple method to characterize the response of the fractional viscoelastic material at different temperatures modeled as a random variable with assigned probability density function (PDF…

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…

Exact frequency response of bars with multiple dampers

The paper addresses the frequency analysis of bars with an arbitrary number of dampers, subjected to harmonically varying loads. Multiple external/internal dampers occurring at the same position along the bar, modelling external damping devices and internal damping due to damage or imperfect connections, are considered. In this context, the challenge is to handle simultaneous discontinuities of the response variables, i.e. axial force/displacement discontinuities at the location of external/internal dampers. Based on the theory of generalized functions, the paper will present exact closed-form expressions of the frequency response under point/polynomial loads, which hold regardless of the n…

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…

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

3D fractional viscoelasticity with applications to structural engineering

Fractional Viscoelasticity Under Combined Stress and Temperature Variations

Nowadays polymeric materials or composites with polymeric matrices are widely used in a very wide range of applications such as aerospace, automotive, biomedical and also civil engineering. From a mechanical point of view, polymers are characterized by high viscoelastic properties and high sensitiveness of mechanical parameters from temperature. Analytical predictions in real-life conditions of mechanical behaviour of such a kind of materials is not trivial for the intrinsic hereditariness that imply the knowledge of all the history of the material at hand in order to predict the response to applied external loads. If temperature variations are also present in the materials, a reliable eval…

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.

The fractional tajimi-kanai model of earthquake gound motion

A fractional viscoelastic non-local Timoshenko beam

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…

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…