Virtual Elements for computational anisotropic crystal plasticity

In this contribution, the Virtual Element Method (VEM) with a linear ansatz is applied to a computational crystal plasticity framework in a micro-structural environment. Furthermore, a simple anisotropic energetic contribution, based on invariantformulations of tensorial deformation measures and structural tensors, is presented for the cubic elastic anisotropy of the underlying crystal structure. The anisotropic elastic formulation recovers the elasticity tensor structure of a cubic material in the limit of small deformations. The authors propose a new stabilization degradation formulation which is purely based on the dissipative response of the problem. Representative examples illustrate the robustness and performance of VEM with regard to locking phenomena in the crystal plasticity framework, when bench-marked against the solutions of classical finite element approaches. Further examples investigate the performance and current limitations of VEM within a crystal plasticity framework, when being applied to heterogeneous microstructures for both, structured element topology as well as flexible element topology. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this paper, the Virtual Element Method (VEM) with a linear ansatz is utilized in a computational crystal plasticity framework in a micro-structural environment. The authors propose a simple anisotropic energetic contribution based on invariant formulations of tensorial deformation measures and structural tensors for the cubic elastic anisotropy of the underlying crystal structure. Additionally, a new stabilization degradation formulation purely based on the dissipative response of the problem is introduced. Representative examples demonstrate the robustness and performance of VEM in addressing locking phenomena and its limitations in heterogeneous microstructures within a crystal plasticity framework.