On material-convective elasto-plasticity

Abstract

A material-convective continuum formulation is presented which differs significantly from the finite elasto-plasticity descriptions of general-purpose finite element simulation tools like Dyna3D, Abaqus, Marc, etc. The material-convective continuum formulation offers physical significance in particular with respect to the geometrical interpretation of the (plastic) deformation tensors—in contrast to the so-called Updated Lagrangian Formulation of general-purpose finite element simulation tools which is unphysical due to its inaccurate (directional non-convective) integration of the (plastic) deformation increments: this inaccurately integrated (plastic) deformation does not obey the geometrical interpretation of proper (plastic) deformation tensors and may even lead to a violation of the first fundamental law of thermodynamics, the conservation of energy. The material-convective time integrals are the reverse of the material-convective time derivatives, and the only material-convective time derivative of a symmetric second-order Eulerian tensor is its Green-Naghdi rate which is rotationally and translationally convected with the material.