Manyanisotropicdamagemodelshavebeenproposedfordifferentmaterials,includingconcrete. The main drawback of the corresponding analyses is that a large number of material parameters is often intro- duced, leading to identification difficulties but also to model complexity and associated numerical difficulties. It is also sometimes difficult to ensure…
Manyanisotropicdamagemodelshavebeenproposedfordifferentmaterials,includingconcrete. The main drawback of the corresponding analyses is that a large number of material parameters is often intro- duced, 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 ra- tio 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 princi- pal 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 differen- tiated, 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.