A large strain anisotropic ductile damage model — Effective driving forces and gradient-enhancement of damage vs. plasticity

Abstract

A novel anisotropic ductile damage model at finite strains is proposed in this work. The model is formulated based on the fictitious configuration concept and includes deformation induced evolution of anisotropic damage properties. As a key contribution, different effective driving forces for both, plasticity and damage are elaborated in the context of a so-called two-surface formulation, i.e. the consideration of two admissible (but not independent) domains — one related to plastic flow and one related to damage evolution. The investigations include the introduction of effective stresses driving plastic flow on the one hand, and effective driving forces related to the evolution of anisotropic damage on the other. In addition and as an alternative to the introduction of effective driving forces, contributions influencing the respective threshold values related to plastic flow and damage evolution are proposed. Specification of the underlying constitutive equations together with the introduction of a suitable algorithmic implementation allows the model to predict experimentally observed material behaviour. Moreover, fundamental properties of the model are discussed by means of non-proportional loading paths generated by combinations of loading under uniaxial tension and simple shear. In view of the simulation of inhomogeneous boundary value problems, the implementation of the model into a finite element formulation is discussed. Since softening, respectively material degradation and necking phenomena, may results in mesh-dependent simulation results, an appropriate regularisation must be included in the model. In this work, gradient-enhancements in the form of a so-called micromorphic approach are included. In particular, gradients of scalar-valued hardening variables related to plasticity and damage are accounted for. A detailed analysis of the necessity of these gradient-enhancements of both, damage and plasticity is carried out based on the proposed multi-surface anisotropic ductile damage model. It turns out that gradient-enhanced regularisation of the damage contribution alone is not sufficient to regularise the problem (and vice versa, i.e. gradient-enhanced regularisation of the plasticity contribution alone is not sufficient as well) but contributions related to both phenomena, i.e. damage and plasticity, need to be regularised.