Modelling of Crack Growth Using a New Fracture Criteria Based Peridynamics

Abstract

Peridynamics (PD) is a nonlocal continuum theory based on integro-differential equations without spatial derivatives. The elongation fracture criterion is implicitly incorporated in the PD theory, and fracture is a natural outcome of the simulation. On the other hand, a new fracture criterion based on the crack opening displacement combined with peridynamic (PD-COD) is proposed. When the relative deformation of the PD bond between two particles reaches the critical crack tip opening displacement of the fracture mechanics, we assume that the bond force vanishes. The new damage rule of fracture criteria similar to the local damage rule in conventional PD is introduced to simulate the fracture. In this paper, first, a comparative study between XFEM and PD is presented. Then, four examples, i.e., a bilateral crack problem, double parallel crack, monoclinic crack, and the double inclined crack are given to demonstrate the effectiveness of the new criterion.

Keywords

• Peridynamic
• Castigliano’s theorem
• Critical extension
• COD
• PD-COD