Element-based coupling modeling of peridynamics and classical continuum mechanics for dynamic brittle fracture

In this work, the hybrid peridynamic and classical continuum mechanical model based on the element-type numerical discretization is used to study the dynamic fracture problem of brittle materials. The weak form of the motion equation for the hybrid model is derived by applying Hamilton's principle. An element-based spatial discretization scheme is set up using the peridynamics-based finite element method (PeriFEM) (Han and Li). The & delta;$$ \delta $$-convergence and m-convergence of the hybrid model are analyzed to verify the numerical convergence and the mesh dependency. The influence of the area of the peridynamic model subdomain and the hybrid model subdomain on the calculation efficiency and accuracy is discussed. And the relationship between the crack propagation speed and the crack branching phenomenon is also investigated. Good agreements are obtained by comparing the crack path and the crack speed profile predicted by the hybrid model with those in the literature. Numerical results verify the ability and efficiency of the hybrid model for dynamic fracture problem.