A simplified orthotropic viscoplasticity theory based on overstress

Abstract

A small strain viscoplasticity theory based on overstress is formulated for orthotropy. Creep and plasticity are not separately accounted for in this “unified” approach, and yield surfaces and loading and unloading conditions are not part of the theory. It contains one state variable, the equilibrium stress, for which an orthotropic growth law is formulated. In constant strain rate loading, the model permits asymptotic solutions which are algebraic expressions independent of the initial conditions. These solutions are useful for identification of material properties and show that the asymptotic stress is composed of viscous (rate-dependent) and plastic (rate-independent) contributions. The theory also permits the modeling of creep, relaxation, rate sensitivity, and tension-compression asymmetry and represents cyclic neutral behavior. The simplified version reduces the needed material constants to a minimum. The elastic stiffness matrix, two material functions which control the rate dependence and the shape of the stress-strain curve, as well as constants which control the rate-independent and rate-dependent asymptotic contributions to the stress, are needed. The properties are illustrated with monotomic and cyclic uniaxial and biaxial numerical experiments.