A damage model based on Kelvin eigentensors and Curie principle

Abstract

A general anisotropic damage model is developed that accounts for the thermodynamics of irreversible processes in the framework of generalized standard materials and Kelvin tensor decomposition. Damage is described by fourth-rank tensors, one per eigenspace of the initial stiffness tensor. Their number thus ranges from two for an initially isotropic material to six for an initially triclinic material. The yield criteria are expressed in terms of a limiting energy for each eigenspace. The second-rank eigentensors (at most six) of the fourth-rank damage tensors define the direction of influence of the damage, while the associated eigenvalues characterize its intensity. These eigentensors evolve during loading, inducing an evolution of the symmetry group of the elastic tensor subject to the constraints of the Curie principle.