On a multiaxial nonlinear hereditary constitutive law for non-ageing materials with fading memory (Q1083265)

A hereditary type complementary power potential is postulated which permits definition of the strain rate tensor in terms of the history and current magnitude of a certain combination of stress and stress deviator components. The strain rate tensor is decomposed into elastic and viscous portions, the latter being further separated into reversible and irreversible parts with the reversible portion being represented by Volterra type integrals. For a material obeying Norton's power law, the three-dimensional nonlinear constitutive equations are derived in terms of two elastic constants and five viscous material parameters which may be determined from creep tests. These equations are applied to the derivation of general nonlinear viscoelastic constitutive relations for a plate element which, in turn, are used to solve the cylindrical time- deflection problem of a long simply supported ice plate subjected to in- plane compressive forces applied along the longitudinal edges. The governing equations are solved numerically, using an incremental approach. An approximate method for the effective numerical treatment of problems involving hereditary type constitutive relations is discussed in detail.