The constitutive relations of elastic-inelastic materials at small strains

Abstract

A set of constitutive relations is presented to describe the elastic-inelastic material behaviour of austenitic steel in the range of small strains, and up to 600°C. This model permits a description of the hardening behaviour in the case of mechanical loading as well as hardening and softening in the case of thermal loading. The loading path may be either monotonic or cyclic. For this purpose, the well-known concepts of isotropic and kinematic hardening are connected within the framework of an internal variable theory. A number of suitably defined internal variables is introduced to describe the transition from isotropic to kinematic hardening behaviour of the material. The model allows for a rate-dependence of the material behaviour when exceeding the yield limit. Therefore the concept of “overstresses” is introduced, where the (real) stresses during inelastic deformations are rate-dependent multiples of the (static) plastic stresses, thus that both stresses coincide in the limit of vanishing velocities (static limit). For some simple examples this model is applied to numerical calculations.