A novel gradient-extended anisotropic two-surface damage-plasticity model for finite deformations

Abstract

Modelling as well as simulation of materials behaving both brittle and/or ductile in connection with anisotropic damage is still a challenging task, especially in the case of finite deformations. This has already been intensively discussed in our recently published work of Reese et al. [1], which, however, uses a different kinematic approach than the one that will be presented here. In addition to the formulation of a constitutive law, a mesh-independent formulation in the presence of large deformations is essential from a computational point of view. Therefore, in the presented work, both a thermodynamically consistent elasto-damage-plasticity material formulation and its gradientextension -based on the invariants of the damage tensor -are discussed, which can be understood as a micromorphic extension following Forest [2]. Thus, although a second order damage tensor is used, only three additional (micromorphic) fields are required to account for the nonlocal nature of damage. Choosing damage itself for the gradient-extension is of course not a unique choice, however, the very good experience of our research group following this approach for different kinds of inelastic and anisotropic material effects (see e.g. [3,4]) motivates this choice.

Efficient gradient enhancements for plasticity with ductile damage in the logarithmic strain space

“…With the help of Eqs. ( 6) and ( 7) also additional tangents can be transformed with the common projection tensor P, as also utilised in (Holthusen et al, 2021(Holthusen et al, , 2022.…”

“…If the gradient-enhancement is placed on the local damage variable ϑ = d, as similarly done in (Horak and Jirásek, 2013;Friedlein et al, 2020;Holthusen et al, 2021), the nonlocal variable is denoted as the global damage d. Due to the affine damage combination from Eq. ( 23), the non-locality in the material model can be simply introduced by combining the truly local damage d loc with the global damage d to the local damage as…”