  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.
