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

• Published in: Computer methods in applied mechanics and engineering Vol. 306; pp. 151 - 174
• Main Author: Shutov, A.V.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2016
• Subjects: Accuracy; Algorithms; Aluminum base alloys; Chromium molybdenum steels; Computation; Finite element method; Implicit time stepping; Incompressibility; Invariance; Kinematic hardening; Mathematical analysis; Mathematical models; Multiplicative elasto-plasticity; Partitioned Euler Backward; Viscoplasticity; Finite element method; Implicit time stepping; 74S05; Partitioned Euler Backward; Kinematic hardening; 65L80; 74C20; Multiplicative elasto-plasticity
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2016.03.045

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. •A model of finite-strain viscoplasticity based on Lion’s approach is considered.•The discretized system of constitutive relations is reduced to a scalar equation.•The approach exploits the notion of the weak invariance of the material model.•The symmetry, incompressibility, and weak invariance are exactly retained.•The accuracy and stability of the algorithm are tested numerically.