Microscale and mesoscale discrete models for dynamic fracture of structures built of brittle material

In this work we present the discrete models for dynamic fracture of structures built of brittle materials. The models construction is based on Voronoi cell representation of the heterogeneous structure, with the beam lattice network used to model the cohesive and compressive forces between the neighboring cells. Each lattice component is a geometrically exact shear deformable beam which can describe large rigid body motion and the most salient fracture mechanisms. The latter can be represented through the corresponding form of the beam constitutive equations, which are derived either at microscale with random distribution of material properties or at a mesoscale with average deterministic values. The proposed models are also placed within the framework of dynamics, where special attention is paid to constructing the lattice network mass matrix as well as the corresponding time-stepping schemes. Numerical simulations of compression and bending tests is given to illustrate the models performance.