Efficient implicit integration for finite-strain viscoplasticity with a nested multiplicative split

TL;DR

This paper introduces an efficient implicit integration algorithm for finite-strain viscoplasticity that preserves weak invariance and inelastic incompressibility, offering comparable accuracy but superior computational efficiency over existing methods.

Contribution

The paper presents a novel implicit integration algorithm for finite-strain viscoplasticity that maintains weak invariance and inelastic incompressibility, improving computational efficiency.

Findings

The new algorithm is first-order accurate and comparable in accuracy to existing methods.

It is computationally more efficient than the Euler Backward method with correction and exponential method.

Numerical tests confirm the algorithm's correctness and efficiency for aluminum alloy and steel models.

Abstract

An efficient and reliable stress computation algorithm is presented, which is based on implicit integration of the local evolution equations of multiplicative finite-strain plasticity/viscoplasticity. The algorithm is illustrated by an example involving a combined nonlinear isotropic/kinematic hardening; numerous backstress tensors are employed for a better description of the material behavior. The considered material model exhibits the so-called weak invariance under arbitrary isochoric changes of the reference configuration, and the presented algorithm retains this useful property. Even more: the weak invariance serves as a guide in constructing this algorithm. The constraint of inelastic incompressibility is exactly preserved as well. The proposed method is first-order accurate. Concerning the accuracy of the stress computation, the new algorithm is comparable to the Euler Backward method with a subsequent correction of incompressibility (EBMSC) and the classical exponential method (EM). Regarding the computational efficiency, the new algorithm is superior to the EBMSC and EM. Some accuracy tests are presented using parameters of the aluminum alloy 5754-O and the 42CrMo4 steel. FEM solutions of two boundary value problems using MSC.MARC are presented to show the correctness of the numerical implementation.