Fracture analysis of orthotropic functionally graded materials using element-based peridynamics

A fracture model of orthotropic functionally graded materials (FGMs) based on element-based peridynamics (EBPD) is proposed. Two-dimensional (2D) orthotropic FGMs use three-node triangular elements to describe the force density of EBPD. Due to the gradient difference of material properties inside the element, the Gauss integral formula is used to average the node performances to the integral point of the element. The equations of motion for EBPD is established, which is also applied to orthotropic FGMs by the Gauss integral formula. The micromodulus coefficient of the EBPD is derived for orthotropic FGMs. The critical strain energy density criterion is used as the failure criterion to simulate the quasi-static and dynamic fracture problems. A series of numerical examples, including displacement analysis, stress analysis, dynamic crack propagation of FGM beam, and crack growth of orthotropic FGMs under four-point bending load, are used to validate the accuracy of the fracture model of orthotropic FGMs. The proposed model can be helpful to the material gradient design for FGMs satisfying certain requirements.