Search results for " viscoelastic"
showing 10 items of 41 documents
Fractional hereditariness of lipid membranes: Instabilities and linearized evolution
2016
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…
Fractional order hereditariness of knee human ligament and tendon
2017
Anterior Cruciate Ligament (ACL) is one of the four major ligaments in the knee, playing a critical role in stabilizing the joint. ACL is highly susceptible to injury, overall during sport activities, often precipitating catastrophic long-term joint outcomes. The ideal replacement graft for a torn ACL would restore native anatomy and function to the knee. Most commonly used autograft and allograft, including patellar tendon (P) and hamstring tendon (H) graft, or bioengineered synthetic grafts, may substantially alter the biomechanics of the knee, permitting a return to only moderate physical activities [1]. Main issues are the sub-optimal graft properties [2] and a still incomplete biomecha…
Theory of heterogeneous viscoelasticity
2015
We review a new theory of viscoelasticity of a glass-forming viscous liquid near and below the glass transition. In our model we assume that each point in the material has a specific viscosity, which varies randomly in space according to a fluctuating activation free energy. We include a Maxwellian elastic term and assume that the corresponding shear modulus fluctuates as well with the same distribution as that of the activation barriers. The model is solved in coherent-potential approximation (CPA), for which a derivation is given. The theory predicts an Arrhenius-type temperature dependence of the viscosity in the vanishing-frequency limit, independent of the distribution of the activatio…
Fractional Derivatives in Interval Analysis
2017
In this paper, interval fractional derivatives are presented. We consider uncertainty in both the order and the argument of the fractional operator. The approach proposed takes advantage of the property of Fourier and Laplace transforms with respect to the translation operator, in order to first define integral transform of interval functions. Subsequently, the main interval fractional integrals and derivatives, such as the Riemann–Liouville, Caputo, and Riesz, are defined based on their properties with respect to integral transforms. Moreover, uncertain-but-bounded linear fractional dynamical systems, relevant in modeling fractional viscoelasticity, excited by zero-mean stationary Gaussian…
Simplified Procedure for Evaluating the Effects of Creep and Shrinkage on Prestressed Concrete Girder Bridges and the Application of European and Nor…
2013
The effects of time-dependent phenomena on concrete prestressed girder bridges are investigated. The study concerns the case of bridges built directly in their final configuration and that of bridges built by a sequence of stages in which geometry, restraints, and loads vary until the final configuration is achieved. An analytical approach based on the principles of aging linear viscoelasticity and the age-adjusted effective modulus method is followed. The paper has two aims: the first is to provide an efficient and simplified tool for the evaluation of the structural response in the early stages of design; the second is to compare the results of the analyses on actual cases of bridges when…
Mathematical modeling and parameters estimation of a car crash using data-based regressive model approach
2011
Author's version of an article in the journal: Applied Mathematical Modelling. Also available from the publisher at: http://dx.doi.org/10.1016/j.apm.2011.04.024 n this paper we present the application of regressive models to simulation of car-to-pole impacts. Three models were investigated: RARMAX, ARMAX and AR. Their suitability to estimate physical system parameters as well as to reproduce car kinematics was examined. It was found out that they not only estimate the one quantity which was used for their creation (car acceleration) but also describe the car's acceleration, velocity and crush. A virtual experiment was performed to obtain another set of data for use in further research. An A…
Finite element method on fractional visco-elastic frames
2016
Viscoelastic behavior is defined by fractional operators.Quasi static FEM analysis of frames with fractional constitutive law is performed.FEM solution is decoupled into a set of fractional Kelvin Voigt elements.Proposed approach could be easily integrated in existing FEM codes. In this study the Finite Element Method (FEM) on viscoelastic frames is presented. It is assumed that the Creep function of the constituent material is of power law type, as a consequence the local constitutive law is ruled by fractional operators. The Euler Bernoulli beam and the FEM for the frames are introduced. It is shown that the whole system is ruled by a set of coupled fractional differential equations. In q…
THE MECHANICAL MODEL OF FRACTIONAL VISCOELASTICITY
2010
Viscoelastic materials have been more and more used nowadays for their low-cost productions as well as for their dissipative capabilities that may be coupled with others, more performing materials, to form complex-type engineering elements. The main feature of viscoelastic behavior is the relaxation of the stress state and the creep of the strain field that may be experienced, respectively, in hard or soft test devices. Such phenomenological consideration has been extensively analyzed yet at the beginning of the twentieth century and simple rheological models representing linear, constitutive, stress-velocity relations of the studied material have been proposed. Moreover the rheological rel…
On the numerical implementation of a 3D fractional viscoelastic constitutive model
2015
The aim of this paper is the implementation of a 3D fraction al viscoelastic constitutive law in a user material subroutine (UMAT) in the finite element software Abaqus. Essential to the implementation of the model is access to the strain history at each Gauss point of each element in a constructive manner. Details of the UMAT and comparison with some analytical results are presented in order to show that the fractional viscoelastic constitutive law has been successfully implemented.
Exact frequency response of bars with multiple dampers
2016
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…