Linearization in nonlinear viscoelasticity and its use in the determination of relaxation moduli

Abstract

A short review is given of the Green-Rivlin theory of nonlinear materials with memory. Small viscoelastic deformation following instantaneous finite elastic response is analysed by linearization of the added viscoelastic deformation. Incompressible, initially isotropic, materials are considered. Such an approach can simplify the analysis of the technologically important problem of stress analysis following sudden loading, which does not fall within the scope of the more common perturbation about a steady or equilibrium strain configuration. The method is applied to the problem of simple tension of a nonlinear viscoelastic rod. Measurement of the mechanical behaviour of real materials is considered. It is shown how material behaviour, in the form of the kernel functions (relaxation moduli) of the linearized constitutive equation, may be determined by a series of two-step simple relaxation tests. Use of the linearization in stress analysis problems is discussed. In addition to being able to determine the kernel functions of the linearized equation by a simple series of experiments, there is the additional practical advantage over the general nonlinear theory of speed of computation.