Nonlinear viscoelasticity of strain rate type: an overview

Abstract

There are some materials in nature that experience deformations that are not elastic. Viscoelastic materials are some of them. We come across many such materials in our daily lives through a number of interesting applications in engineering, material science and medicine. This article concerns itself with modelling of the nonlinear response of a class of viscoelastic solids. In particular, nonlinear viscoelasticity of strain rate type, which can be described by a constitutive relation for the stress function depending not only on the strain but also on the strain rate, is considered. This particular case is not only favourable from a mathematical analysis point of view but also due to experimental observations, knowledge of the strain rate sensitivity of viscoelastic properties is crucial for accurate predictions of the mechanical behaviour of solids in different areas of applications. First, a brief introduction of some basic terminology and preliminaries, including kinematics, material frame-indifference and thermodynamics, is given. Then, considering the governing equations with constitutive relationships between the stress and the strain for the modelling of nonlinear viscoelasticity of strain rate type, the most general model of interest is obtained. Then, the long-term behaviour of solutions is discussed. Finally, some applications of the model are presented.

Deformation Mechanism of Amorphous Plasticized Poly(vinyl butyral)

“…The sample exhibits strong viscoelasticity in this strain rate range. The modulus and stress increase with strain rate, while fracture strain decreases, similar to common viscoelastic materials. − The fracture stress is about 30 MPa, and it weakly depends on the strain rate, which is consistent with previous results. − , …”

Stress-rate-type strain-limiting models for solids resulting from implicit constitutive theory

“…We provide a brief introduction of the mathematical background covering fundamental equations that form the basis of continuum mechanics, and the formulation of implicit constitutive theory. Similar reviews can also be found in [2,10,14,15].…”

Pure bending of an elastic prismatic beam made of a material with density-dependent material parameters

“…The dependence of material moduli on the density leads to nonlinear models even in the small strain range, and the impact of this nonlinearity on the solution of the classical boundary value problems of elastic solids must be carefully assessed. (The same holds also for inelastic materials with nonlinearities in the small strain range, see, for example, Rajagopal [22], Bulíček et al [23], or Şengül [24,25] for some studies in this direction. See also Rajagopal and Wineman [26] for a study regarding a viscoelastic solid with density-dependent material moduli.)…”