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 provide an overview of the subject of nonlinear viscoelastic solids for researchers who are interested in studying the mechanics of these materials. The article begins with a review of topics from linear viscoelasticity that are pertinent to the understanding of nonlinear viscoelastic behavior. It then discusses the topics that enter into the formulation of constitutive equations for isotropic, transversely isotropic and orthotropic nonlinear viscoelastic solids. A number of specific forms of constitutive equations have been proposed in the literature and these are discussed. Attention is restricted to constitutive equations that are phenomenological rather than molecular in origin. The emphasis is then on nonlinear single integral finite linear viscoelastic and Pipkin—Rogers constitutive equations, the latter containing the quasi-linear viscoelastic model used in biomechanics of soft tissue. Expressions for the Pipkin—Rogers model are provided for isotropy, transverse isotropy and orthotropy. The constitutive equations are then applied to the description of homogeneous triaxial stretch and simple shear histories. The special case of uniaxial stretch histories is analyzed in detail. There is a discussion of the deviation from linear behavior as nonlinear effects become important. Non-homogeneous deformations are considered next. The combined tension and torsion of a solid cylinder on an incompressible, isotropic nonlinear viscoelastic solid is discussed in detail because of its importance in experiments involving viscoelastic materials. A large number of solutions to boundary value problems have appeared in the literature and many of these are summarized. The article concludes with comments about interesting topics for further research.

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Skeletal muscle is composed of muscle fibers and an extracellular matrix (ECM). The collagen fiber network of the ECM is a major contributor to the passive force of skeletal muscles at high strain. We investigated the effect of aging on the biomechanical and structural properties of epimysium of the tibialis anterior muscles (TBA) of rats to understand the mechanisms responsible for the age-related changes. The biomechanical properties were tested directly in vitro by uniaxial extension of epimysium. The presence of age-related changes in the arrangement and size of the collagen fibrils in the epimysium was examined by scanning electron microscopy (SEM). A mathematical model was subsequently developed based on the structure-function relationships that predicted the compliance of the epimysium. Biomechanically the epimysium from old rats was much stiffer than that of the young rats. No differences were found in the ultrastructure and thickness of the epimysium or size of the collagen fibrils between young and old rats. The changes in the arrangement and size of the collagen fibrils do not appear to be the principal cause of the increased stiffness of the epimysium from the old rats. Other changes in the structural composition of the epimysium from old rats likely has a strong effect on the increased stiffness. The age-related increase in the stiffness of the epimysium could play an important role in the impaired lateral force transmission in the muscles of the elderly.

Poisson's ratio in viscoelastic solids is in general a time dependent (in the time domain) or a complex frequency dependent quantity (in the frequency domain). We show that the viscoelastic Poisson's ratio has a different time dependence depending on the test modality chosen; interrelations are developed between Poisson's ratios in creep and relaxation. The difference, for a moderate degree of viscoelasticity, is minor. Correspondence principles are derived for the Poisson's ratio in transient and dynamic contexts. The viscoelastic Poisson's ratio need not increase with time, and it need not be monotonic with time. Examples are given of material microstructures which give rise to designed time dependent Poisson's ratios.

Classical theories of elasticity assume that the Cauchy stress in the material depends on the deformation gradient of particles in the current configuration. Such as assumption can usually be motivated by the presence of a single micromechanism. Here we consider the possibility that as the material is deformed an additional micromechanism might come into play and have a role in determining the Cauchy stress. We show that "inelastic" behavior of some materials can be explained within the context of such a theory. To illustrate our ideas, we use the ideas of scission and reforming of networks within the context of polymeric materials. The theory is of course much more general and can be used to describe the mechanics of materials in which microstructural changes are induced due to deformations.

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