Non standard thermodynamics framework for robust computations with induced anisotropic damage

Abstract : Many anisotropic damage models have been proposed for different materials, including concrete. The main drawback of the corre- sponding analyses is that a large number of material parameters is often introduced, leading to identification difficulties but also to model complex- ity and associated numerical difficulties. It is also sometimes difficult to ensure the continuity of the stresses if the quasi-unilateral effect of micro- cracks closure and the dissymmetry tension/compression are represented. In order to solve those difficulties, one proposes to write the damage models in a specific non standard thermodynamics framework. The dam- age 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 meanning: 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 non standard 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 non proportional. This extends then to induced anisotropy the isotropic case property of a positive damage rate as a sufficient condition for the ther- modynamics second principle to be fulfilled. Altogether with the fact that the thermodynamics potential can be con- tinuously differentiated, the anisotropic damage model for concrete (build in this framework) 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.
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Rodrigue Desmorat, Fabrice Gatuingt, Frédéric Ragueneau. Non standard thermodynamics framework for robust computations with induced anisotropic damage. International Journal of Damage Mechanics, SAGE Publications, 2010, 19 (1), pp.53-73. ⟨10.1177/1056789509104839⟩. ⟨hal-00994281⟩



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