Nonstandard Thermodynamics Framework for Robust Computations with Induced Anisotropic Damage

Many anisotropic damage models have been proposed for different materials, ductile as well as quasi-brittle. The main drawback of the corresponding analyzes is that a large number of material parameters is often introduced, leading to identification difficulties and 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. In order to solve those difficulties, one proposes to write the damage models in a specific nonstandard thermodynamics framework. The damage states are represented by a symmetric second-order tensor and the damage rate is assumed governed by a positive second-order tensor having a clear meaning: the absolute or the positive value of the plastic strain rate tensor for ductile materials, the positive part of the total strain tensor in quasi-brittle materials. Such a nonstandard feature makes the proof of the the positivity of the intrinsic dissipation necessary. This important proof is given in the considered framework for any damage law ensuring (anisotropic) damage increase and for any case, 3D, proportional or nonproportional. This extends then to induced anisotropy the isotropic case property of a positive damage rate as a sufficient condition for the thermodynamics second principle to be fulfilled. Altogether with the fact that the thermodynamics potential can be continuously differentiated, the example of an anisotropic damage model for concrete (build in this framework) is given. It allows for robust finite element implementation. Both space (classical nonlocal with internal length, nonlocal with internal time) and time regularizations (visco- or delay-damage) are used and applied to quasi-static and dynamic cases. Examples on concrete and reinforced concrete structures are given.