Loading rate effects on dynamic failure of quasi-brittle solids: Simulations with a two-scale damage model

•A two-scale damage model based on the dynamic microcrack propagation.•Finite Element simulations of dynamic failure tests in concrete, polymer and rock specimens.•Study of loading rate influence on the fracture mode and the crack branching process.•Good agreement with experimental observations. In this contribution we present numerical simulations of rapid failure in brittle materials using a dynamic damage law. The model is deduced from a microscopic Griffith-type criterion describing the dynamic mode I propagation of microcracks, using a homogenization method based on asymptotic expansions. The resulting damage law is sensitive to the loading rate that influences the macroscopic failure modes. Finite Element simulations are performed in order to identify the model predictions and the obtained numerical results are compared with the experimental ones. Compact tension and L-shape specimen tests for concrete materials, compact compression test for the PMMA brittle polymers and Kalthoff impact test for limestone rocks are considered in the numerical simulations. We show that the loading rate essentially determines the macroscopic crack trajectory and the associated branching patterns. The obtained results are in good agreement with those reported in the experimental works.