Dual-variable-horizon peridynamics and continuum mechanics coupling modeling and adaptive fracture simulation in porous materials

In this paper, we present a hybrid dual-variable-horizon peridynamics/continuum mechanics modeling approach and a strength-induced adaptive coupling algorithm to simulate brittle fractures in porous materials. Peridynamics theory is promising for fracture simulation since it allows discontinuities in the displacement field. However, they remain computationally expensive. Besides, there exists the surface effect in peridynamics due to the incomplete neighborhoods near the boundaries, including the outer boundaries and the boundaries of inner pores in porous materials. The proposed approach couples continuum mechanics and peridynamics into a closed equation system and an adaptive algorithm is developed to activate the peridynamics according to a strength criterion. In addition, the surface effect is corrected by introducing an improved peridynamic model with dual and variable horizons. We conduct the simulations using the relevant discretization scheme in each domain, i.e., the discontinuous Galerkin finite-element in the peridynamic domain and the continuous finite-element in the continuum mechanics domain. Two-dimensional numerical examples illustrate that successful fracture simulations of random porous materials can be achieved by this approach. In addition, the impact of distribution and size of pores on the fractures of porous materials is also investigated.