Intrinsic dissipation of a modular anisotropic damage model: Application to concrete under impact

Based on the mathematical proof of the positivity of the dissipation due to anisotropic damage, different numerical scheme to compute such a dissipation in concrete structures are proposed. The positivity of intrinsic dissipation for the considered modular anisotropic damage model is first checked in the case of Willam non-proportional loading test, then checked for different impact tests on concrete structures. Both the consequences of the modeling of the strain rate effect in tension (from visco-damage) and of the damage deactivation (micro-cracks closure) for alternated loadings are studied.