Numerical strategies for variational updates in large strain inelasticity with incompressibility constraint

Abstract

In finite deformation inelasticity, one often has to deal with the incompressibility constraint. In the past, this was dealt with using, for example, an exponential mapping approach, which yields exact volume preservation in plastic deformations. In this article however, the special-linear update approach by Hurtado et al. The special-linear update: An application of differential manifold theory to the update of isochoric plasticity flow rules, Int J Numer Methods Eng. 2014;97(4):298-312, which utilizes a projection method to fulfill the incompressibility constraint is used. The model is applied to isotropic plasticity by a novel approximation of the logarithm and treats kinematic hardening without losing the symmetry of the internal variables. The model results are compared to models utilizing an exponential mapping approach in numerical experiments.

A thermomechanical finite strain shape memory alloy model and its application to bistable actuators

“…To deal with the constraint in C i , we employ a strategy using a projection of C i into the space of unimodular tensors, which was introduced by Hurtado et al [21] for crystal plasticity. Our approach here closely follows the approach presented in Sielenkämper et al [44]. First, we express C i in terms of the unconstrained inelastic auxiliary right Cauchy-Green tensor Ĉi :…”

“…The energies as well as the dissipation potential can be seen as an extension of Sedlak et al [42] to the finite strain case. Because the satisfaction of the incompressibility of inelastic strains for finite strains is not as straightforward as for the small strain case, a projection method developed for plasticity is incorporated into the model (see Hurtado et al [21] and Sielenkämper et al [44]). Further, due to the character of the energies used in this model, special numerical treatment is necessary to solve the model equations using a Newton scheme.…”