Cosserat constitutive theory and one of its higher-order forms: A rediscussion on the mesh dependence problem

When the finite element method (FEM) is adopted for studying strain localization problems, the mesh dependence phenomenon often ensues. The occurrence of mesh dependency will reduce the reliability of FEM simulations, so it is still worth studying. Herein, a constitutive model with decent mesh stability named the multiscale Cosserat (MC) model which contains higher-order rotation variables based on the conventional Cosserat (CC) theory, was introduced. The theory derivation indicates that the MC model has an extra internal length scale vector D_q that can consider the microscopic geometrical characteristics of the simulated material and can easily regress to the conventional Cosserat model when D_q = 0. After revisiting the mesh dependence problem through numerical simulations of plane strain compression tests, the mechanisms and advantages of the CC and MC models in solving the mesh dependence problem were discussed. The analysis demonstrated that the CC theory can alleviate the mesh dependence problem but cannot eliminate it; when the divergence of the computation occurs, due to a stricter accuracy requirement for convergence, the computation result of the MC model tends to stabilize along with the refinement of the elements. The mesh advantage of the MC model is influenced by both the length scales l and D_q. This study can provide new insight into understanding the mesh dependence problem, and the MC model introduced here is a potential model for comprehensively eliminating the influence of mesh dependence problems.