A continuum anisotropic damage model with unilateral effect

A continuum damage mechanics model has been derived within the framework of irreversible thermodynamics with internal variables in order to describe the behaviour of quasi-brittle materials under various loading paths. The anisotropic character induced by the progressive material degradation is explicitly taken into account, and the Helmholtz free energy is a scalar function of the basic invariants of the second order strain and damage tensors. The elastic response varies depending on the closed or open configuration of defects. The constitutive laws derived within the framework of irreversible thermodynamics theory display a dissymmetry as well as unilateral effects under tensile and compressive loading conditions. This approach verifies continuity and uniqueness of the potential energy. An application to uniaxial tension-compression loading shows a good adequacy with experimental results when available, and realistic evolutions for computed stresses and strains otherwise