The microstructural design has an essential effect on the fracture response of brittle materials. We present a stochastic bulk damage formulation to model dynamic brittle fracture. This model is compared with a similar interfacial model for homogeneous and heterogeneous materials. The damage models are rate-dependent, and the corresponding damage evolution includes delay effects. The delay effect provides mesh objectivity with much less computational efforts. A stochastic field is defined for material cohesion and fracture strength to involve microstructure effects in the proposed formulations. The statistical fields are constructed through the Karhunen-Loeve (KL) method. An advanced asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used to discretize the final system of coupled equations. Application of the presented formulation is shown through dynamic fracture simulation of rock under a uniaxial compressive load. The final results show that a stochastic bulk damage model produces more realistic results in comparison with a homogenizes model.

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