Thermodynamics framework for robust computations of loading-induced anisotropic damage

Many anisotropic damage models have been proposed for different materials, including concrete. The main drawback of the corresponding analyses is that a large number of material parameters is often introduced, leading to identification difficulties but also to model complexity and associated numerical difficulties. It is also sometimes difficult to ensure the continuity of the stresses if the quasi-unilateral effect of microcracks closure and the dissymmetry tension/compression are represented. We consider here an anisotropic damage model with a restricted number of material parameters (5 including the Young’s modulus and Poisson’s ratio of the initially isotropic material) and built in the thermodynamics framework. The large dissymmetry of tension/compression response of concrete is due to the loading induced damage anisotropy. A non standard thermodynamics framework is used with damage states represented by a symmetric second order tensor and with a damage rate governed by the positive part of the strain tensor. The proof of the positivity of the intrinsic dissipation is given for any damage law ensuring (anisotropic) damage increase - in terms of positive principal values of the damage rate tensor. This extends then to induced anisotropy the isotropic case property of a positive damage rate. Altogether with the fact that the thermodynamics potential can be continuously differentiated, the considered anisotropic damage model allows for robust Finite Element implementation. Both space and time regularizations are used and applied to quasi-static and dynamic cases. Examples on concrete and reinforced concrete structures are given, with the consideration of either nonlocal Mazars criterion or of Mazars criterion regularized with viscous damage.