A three-dimensional (3D) micro-potential-based peridynamics model for deformation and fracture in solid materials

Abstract

In this work, an innovative three-dimensional (3D) micro-potential-based peridynamics model is developed, and its applications for modeling deformation and fracture of solid materials are studied. In the present micro-potential-based peridynamics, a square measure of bond deformation is considered within peridynamics framework, and a 3D nonlocal strain tensor is constructed, including the nonlocal shear strain and the nonlocal volumetric strain. We assume that the micro potential energy generated by particle deformation conforms to the Xu–Needleman potential function, then the micro-potential-based peridynamics constitutive model is established. A bond failure criterion based on the energy release rate is established for the three-dimensional micro-potential-based peridynamics model and the critical stretch of bonds is derived, then the discrete form of the numerical implementation of the model is given. The bond force models obtained by present micro-potential-based peridynamics and existing peridynamics models are compared and investigated. Finally, Mode I, II, and III cracks are selected to verify the current 3D micro-potential-based peridynamics model in the simulation of deformation and fracture, as the nonlocal strain, crack nucleation, and propagation characteristics.