Nonlinear theory of viscoelastic isotropic bodies

Abstract

The theory of viscoelasticity and its development and application in various fields of technology and construction have gained in importance in the last few years. In particular, this has been brought about by the extensive use of polymeric materials in industry and construction. A large number of papers on the nonlinear theory of elasticity and viscoelasticity by soviet and foreign scientists have been published, among which should be noted the monographs [1-6]. We derive below the fundamental relations between the components of the stress and strain tensors for viscoelastic isotropic bodies in the case of a physical nonlinearity~ i. BASIC ASSUMPTIONS AND HYPOTHESES The theory of linear viscoelasticity is based on the effect of memory, i.e.~ a linear integral relation between stresses and strains, and has been treated in a number of monographs [i, 2, 4]. The nonlinear theory of viscoelasticity, in spite of its similarity to the linear theory, has still not received its complete and final development. Using the hypothesis of memory~ the relations between stresses and strains in the linear approximation for a viscoelastic isotropic body can be written in the form