Nonlinear Constitutive Laws in Viscoelasticity

@article{Drapaca2007NonlinearCL,
  title={Nonlinear Constitutive Laws in Viscoelasticity},
  author={Corina S. Drapaca and Sivabal Sivaloganathan and Giuseppe Tenti},
  journal={Mathematics and Mechanics of Solids},
  year={2007},
  volume={12},
  pages={475 - 501}
}
The theory of viscoelasticity appears to play a central role in the description of materials which exhibit time dependent stress—strain behavior. Various materials like polymers, some soft biological tissues, and various foods have been already successfully modeled as nonlinear viscoelastic materials.The literature in these application areas is replete with different, seemingly unconnected nonlinear viscoelastic models. The aim of the present paper is to review the classical nonlinear… Expand

Figures from this paper

Nonlinear Viscoelastic Solids—A Review
Elastomers and soft biological tissues can undergo large deformations and exhibit time dependent behavior that is characteristic of nonlinear viscoelastic solids. This article is intended to provideExpand
A formulation to model the nonlinear viscoelastic properties of the vascular tissue
Nearly all soft tissues, including the vascular tissue, present a certain degree of viscoelastic material response, which becomes apparent performing multiple relaxation tests over a wide range ofExpand
Modified constitutive equation for quasi-linear theory of viscoelasticity
The constitutive equation of the quasi-linear theory of viscoelasticity is modified with the view to simplify our understanding of the physical meaning of numerous kernel functions. In the resultingExpand
Nonlinear viscoelastic membranes
  • A. Wineman
  • Computer Science, Mathematics
  • Comput. Math. Appl.
  • 2007
TLDR
A numerical method of solution is presented that combines methods for solving nonlinear Volterra integral equations and nonlinear ordinary differential equations and some properties of the equations are discussed that are related to the possibility that there may exist a critical time when the solution develops multiple branches. Expand
A nonlinear integral model for describing responses of viscoelastic solids
Abstract In this paper we develop a model as well as carry out experiments to test the efficacy of the model, for a class of non-aging isotropic viscoelastic solids. We fashion a nonlinear integralExpand
On modelling nonlinear viscoelastic effects in ligaments
Experiments in human ligaments revealed that the rate of stress relaxation in such materials is strain dependent. This nonlinear behavior requires therefore a modified description of the standardExpand
On modelling nonlinear viscoelastic effects in ligaments.
TLDR
The structural model presented herein is based on a local additive decomposition of the stress tensor into initial and non-equilibrium parts as resulted from the assumed structure of the free energy density function that generalizes Kelvin-Voigt nonlinear viscous models. Expand
A Brief Review of Elasticity and Viscoelasticity for Solids
TLDR
An overview of the subject for both elastic and viscoelastic materials is provided, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging, and some applications for these constitutive equations. Expand
A Brief Review of Elasticity and Viscoelasticity
Abstract : There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental, including uses in civil engineering, the food industry land mineExpand
On thermodynamically consistent constitutive equations for fiber-reinforced nonlinearly viscoelastic solids with application to biomechanics
Abstract In this paper, we are interested in developing thermodynamically consistent constitutive equations for fiber-reinforced nonlinearly viscoelastic bodies, in particular for transverselyExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 65 REFERENCES
Fractional-order relaxation laws in non-linear viscoelasticity
Viscoelastic constitutive equations are constructed by assuming that the stress is a nonlinear function of the current strain and of a set of internal variables satisfying relaxation equations ofExpand
Molecular origins of nonlinear viscoelasticity
Polymer melts are discussed in terms of relationships between their nonlinear viscoelasticity and molecular structure. The challenges of making nonlinear measurements and the rheometers available forExpand
Mechanical Response of Polymers: An Introduction
Preface 1. Discussion of response of a viscoelastic material 2. Constitutive equations for one-dimensional response of viscoelastic materials: mechanical analogs 3. Constitutive equations forExpand
Nonlinear Viscoelasticity for Short Time Ranges
Abstract : Approximate constitutive equations for nonlinear viscoelastic incompressible materials under small finite deformation and for short time ranges are derived. The error bound of such aExpand
A single integral finite strain viscoelastic model of ligaments and tendons.
TLDR
A general continuum model for the nonlinear viscoelastic behavior of soft biological tissues was formulated and the idea of conversion from one material to another (at a microscopic level) was introduced to model the non linear behavior of ligaments and tendons. Expand
Yieldlike response of a compressible nonlinear viscoelastic solid
Several authors have shown that many aspects of the yieldlike response of polymers can be described by the constitutive framework of nonlinear viscoelasticity. This arises through the use of aExpand
Lectures on Viscoelasticity Theory
I. Viscoelastic Response in Shear.- II. Fourier and Laplace Transforms.- III. Relations Between Modulus and Compliance.- IV. Some One-Dimensional Dynamical Problems.- V. Stress Analysis.- VI. ThermalExpand
Parameter estimation using the quasi-linear viscoelastic model proposed by Fung.
TLDR
The parameter tau 1, governing the fast viscous phenomena, is found to be subject to the largest errors. Expand
A mathematical theory of the mechanical behavior of continuous media
TLDR
Until not long ago continuum mechanics meant to most people the theories of inviscid and linearly viscous fluids and of linearly elastic solids, but nowadays they are only of limited use, because large deformations occur easily in the materials these theories are intended to describe. Expand
Foundations of Linear Viscoelasticity
The classical linear theory of viscoelasticity was apparently first formulated by Boltzmann1 in 1874. His original presentation covered the three-dimensional case, but was restricted to isotropicExpand
...
1
2
3
4
5
...