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Mathematics and Mechanics of Solids
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Response of Anisotropic Nonlinearly Viscoelastic Solids

K.R. Rajagopal

Department of Mechanical Engineering, Texas A&M University, College Station, TX-77845, USA

A.S. Wineman

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI-48109, USA

Despite the technological relevance of anisotropic nonlinear viscoelastic solids, little effort has been expended in the development of specific constitutive theories. In this study we develop a constitutive model for describing the nonlinear response of anisotropic viscoelastic solids that might be well suited to describe the response of biological and geological solids. The model is an integral model that takes into account the history of deformation of the body. Using the model a few boundary value problems are studied, namely the time dependent extension and shearing of such bodies.

Key Words: anisotropy • nonlinear viscoelasticity • constitutive equations • extension • shear

This version was published on July 1, 2009

Mathematics and Mechanics of Solids, Vol. 14, No. 5, 490-501 (2009)
DOI: 10.1177/1081286507085377
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