An innovative bond–based peridynamic model for fracture analysis of orthotropic materials

Fracture analysis of orthotropic materials presents a persistent challenge in computational mechanics, particularly in bond–based peridynamics (BB–PD) framework. This challenge arises from the special material properties of orthotropic materials, presenting difficulties in accurately simulating the mechanical behavior and discerning fracture modes. In particular, the neglect of fracture parameters that profoundly affect the fracture behavior has resulted in an insufficient study of the fracture mechanisms for orthotropic materials. To address this issue, a novel BB–PD model for orthotropic materials was proposed, accompanied by the development of an energy–based failure criterion. The presented BB–PD model has no material parameter limitations and can accurately capture the deformation of orthotropic materials. The energy–based failure criterion considers the variation of fracture energy in different directions and fracture modes, ensuring that the PD calculated fracture energies align with their corresponding theoretical values. To validate the effectiveness of the developed BB–PD model and failure criterion, several numerical examples were performed, including convergence analysis, deformation analysis, and three quasi-static fracture analyses. The results demonstrate that the presented model and failure criterion can accurately predict material deformation and fracture. Furthermore, analysis of fracture modes indicates that the ratio of mode I and mode II fracture energies significantly influences crack paths and fracture modes in orthotropic materials.