FINITE DEFORMATION CONSTITUTIVE-EQUATIONS AND A TIME INTEGRATION PROCEDURE FOR ISOTROPIC, HYPERELASTIC VISCOPLASTIC SOLIDS

Constitute equations for finite deformation, isotropic, elastic-viscoplastic solids are formulated. The concept of a multiplicative decomposition of the deformation gradient into an elastic and a plastic part is used. The constitutive equation for stress is a hyperelastic relation in terms of the logarithmic elastic strain. Since the material is assumed to be isotropic in every local configuration determined by the plastic part of deformation gradient, the internal variables are necessarily scalars. We use a single scalar as an internal variable to represent the isotropic resistance to plastic flow offered by the internal state of the material. The constitutive equation for stress is often expressed in a rate form, and for metals it is common to approximate this rate equation, under the assumption of infinitesimal elastic strains, to arrive at a hypoelastic equation for the stress. Here, we do not express the stress constitutive equation in a rate form, nor do we make this approximative assumption. For the total form of the stress equation we present a new implicit procedure for updating the stress and other relevant variables. Also, the principle of virtual work is linearized to obtain a consistent, closed-from elasto-viscoplastic tangent operator (the 'Jacobian') for use in solving for global balance of linear momentum in implicit, two-point, deformation driven finite element algorithms. The time integration algorithm is implemented in the finite element program ABAQUS. To check the accuracy and stability of the algorithm, some representative problems involving large, pure elastic and combined elastic-plastic deformations are solved. © 1990.