A thermodynamically and variationally consistent class of damage-type cohesive models

Abstract

A novel class of cohesive constitutive models suitable for the analysis of material separation such as that related to cracks, shear bands or delamination processes is presented. The proposed framework is based on a geometrically exact description (finite deformation) and it naturally accounts for material anisotropies. For that purpose, a Helmholtz energy depending on evolving structural tensors is introduced. In sharp contrast to previously published anisotropic cohesive models with finite strain kinematics based on a spatial description, all models belonging to the advocated class are thermodynamically consistent, i.e., they are rigorously derived by applying the Coleman and Noll procedure. Although this procedure seems nowadays to be standard for stress–strain-type constitutive laws, this is not the case for cohesive models at finite strains. An interesting new finding from the Coleman and Noll procedure is the striking analogy between cohesive models and boundary potential energies. This analogy gives rise to the introduction of additional stress tensors which can be interpreted as deformational surface shear. To the best knowledge of the authors, those stresses which are required for thermodynamical consistency at finite strains, have not been taken into account in existing models yet. Furthermore, the additional stress tensors can result in an effective traction-separation law showing a non-trivial stress-free configuration consistent with the underlying Helmholtz energy. This configuration is not predicted by previous models. Finally, the analogy between cohesive models and boundary potential energies leads to a unique definition of the controversially discussed fictitious intermediate configuration. More precisely, traction continuity requires that the interface geometry with respect to the deformed configuration has to be taken as the average of both sides. It will be shown that the novel class of interface models does not only fulfill the second law of thermodynamics, but also it shows an even stronger variational structure, i.e., the admissible states implied by the novel model can be interpreted as stable energy minimizers. This variational structure is used for deriving a variationally consistent numerical implementation.