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 ÿnite strain. A mixed strain element with one-point quadrature and hourglass control at moderate ÿnite 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, 1 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 e cient form.In addition, with the introduction of the natural co-ordinate system, a new deÿnition 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. ?

A 2.5D finite element model for bending and straightening in continuous casting of steel slabs

“…where J 2 = − 1 2ˆ ijˆ ij is the second invariant of deviatoric stress tensor and¯ = 2 3˙ ij˙ ij the equivalent (mechanical) strain rate. The relation (16)…”

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