Efficient implicit integration for finite-strain viscoplasticity with a nested multiplicative split
For researchers in computational mechanics, this algorithm improves computational efficiency for finite-strain viscoplasticity simulations while preserving weak invariance and inelastic incompressibility.
The paper presents an efficient implicit integration algorithm for finite-strain viscoplasticity with a nested multiplicative split, achieving comparable accuracy to existing methods (Euler Backward and exponential method) while being computationally superior. Accuracy tests use aluminum alloy 5754-O and 42CrMo4 steel parameters.
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.