Abstract
We propose a method for evaluating the macroscopic strength and toughness of heterogeneous brittle materials by numerical analyses of microstructures. The method is based on the mathematical homogenization in conjunction with the theoretical framework of material instability. The hybrid variational formulation, which allows us to approximate the displacement in each finite element independently, is adopted for discontinuous deformation of microstructures. Then, the overall collapse of microstructure informs us of the orientation of discontinuous surfaces. The performance of the method is well demonstrated by representative numerical examples.
