A mixed strain element method for pressure-dependent elastoplasticity at moderate finite strain

Abstract

This paper presents a framework to describe a mixed element method in the context of pressure-dependent elastoplasticity at moderate finite strain. A mixed strain element with one-point quadrature and hourglass control at moderate finite strain is developed on the basis of the Hu–Washizu principle and the co-rotational formulation. The element is formulated with reference to the so-called natural co-ordinate system, which allows to derive the consistent tangent modulus matrix and the single step backward Euler integration scheme at the element quadrature point for pressure-dependent elastoplasticity in an elegant and numerically efficient form. In addition, with the introduction of the natural co-ordinate system, a new definition of internal state variable for the pressure-dependent elasto-plasticity is proposed to allow for the simultaneous description of the two strain hardening/softening paths in tension and compression. Numerical examples are given to demonstrate the performance of the mixed element method presented in this paper. © 1998 John Wiley & Sons Ltd.