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

•We compute the dissipation due to anisotropic damage in concrete structures.•The positivity of intrinsic dissipation for the considered modular anisotropic damage model is first checked.•The Willam non-proportional laoding test has been computed.•Then checked for different impact tests on concrete structures.•Comparisons with experimental results for a dynamic Brazilian are made.

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.