Multiscale modeling of rapid failure in brittle solids: Branching instabilities

The contribution presents results on the modeling of fracture instabilities with a dynamic two-scale damage approach. The evolution law for damage is deduced by homogenization from small-scale descriptions of mode I dynamic propagation of micro-cracks. The model is sensitive with respect to the size of the microstructure through a length parameter present in the damage law. We study the macroscopic failure evolution in brittle solids and the development of associated instabilities like micro-branching. The results of numerical simulations for a reduced-size specimen are compared with experimental results for tensile fracture of PMMA and it is shown that the damage model is able to reproduce the observed micro-branching instabilities and the corresponding crack speed evolutions.