A new damage model for rapid shear failure in brittle solids is constructed in the present contribution using a two-scale approach. The model is obtained by asymptotic homogenization from microstructures with dynamically evolving microcracks, in mode II, with unilateral contact and friction conditions on their lips. The analysis of the local effective response of the model reveals strain-rate and microstructural size effects and the influence of the small-scale friction. Results of numerical simulations for mode II brittle failure of PMMA specimens under impact loading are presented and compared with the experimental data. The failure evolution is found to be in good agreement with that reported in the experiments.