A Constitutive Equation for Non-Linear, Compressible Viscoelastic Materials with Fading Memory

Summary

Numerous proposals have been made for time-dependent stress-strain relationships of viscoelastic materials in order to describe creep and relaxation and their application to structures. These differ or they are even contradictory in their assumptions, results, validity and compactness. Basing on the principles of Rational Mechanics for simple, isotropic solids, using representation theorems for the functionals and expansions about theorems for the functionals and expansions about the “rest-history” and formulating a constraint condition for the compressibility a generalized constitutive equation is derived for geomtrical and physical nonlinear behaviour of materials, in which other proposed relations are included as special cases.