A comparative study of micromorphic gradient-extensions for anisotropic damage at finite strains

TL;DR

The paper tackles localization in finite-strain anisotropic damage by regularizing tensor-valued internal variables using micromorphic gradient-extensions. It compares three gradient-extensions—A with six nonlocal degrees of freedom, B with three, and C with two—within a common local damage framework and volumetric-deviatoric separation, deriving explicit nonlocal damage driving forces for each. Numerical experiments across four structural tests show that the two-degree-of-freedom (model C) regularization nearly matches the full six-DOF model (model A) in load-displacement response and damage patterns, while a three-DOF approach (model B) tends to dissipate more energy and alter crack morphology. The findings support using reduced gradient-extensions as efficient, accurate regularization strategies for anisotropic damage at finite strains and point to future experimental validation and extension to other localization phenomena.

Abstract

Modern inelastic material model formulations rely on the use of tensor-valued internal variables. When inelastic phenomena include softening, simulations of the former are prone to localization. Thus, an accurate regularization of the tensor-valued internal variables is essential to obtain physically correct results. Here, we focus on the regularization of anisotropic damage at finite strains. Thus, a flexible anisotropic damage model with isotropic, kinematic, and distortional hardening is equipped with three gradient-extensions using a full and two reduced regularizations of the damage tensor. Theoretical and numerical comparisons of the three gradient-extensions yield excellent agreement between the full and the reduced regularization based on a volumetric-deviatoric regularization using only two nonlocal degrees of freedom.

Figures (27)

• Figure 1: Geometry and boundary value problem of the plate with hole specimen.
• Figure 2: Mesh convergence studies for the plate with hole specimen and model comparison. The forces are normalized with respect to the maximum force of the finest mesh (14752 elements) of model B with $F_\text{max} = 5.0767 \times 10^4~[N]$.
• Figure 3: Contour plots of the normal and shear components of the damage tensor for the plate with hole specimen at the end of the simulation.
• Figure 4: Comparison of the force-displacement curves of the anisotropic and isotropic computation for the plate with hole specimen (14752 elements). The forces are normalized with respect to the maximum force of the anisotropic computation of model B with $F_\text{max} = 5.0767 \times 10^4~[N]$.
• Figure 5: Comparison of the damage contour plots of the anisotropic and isotropic computation for the plate with hole specimen by a difference plot of the isotropic damage value $D$ compared to the normal components of the anisotropic damage tensor $D_{xx}$ and $D_{yy}$.