A stability-enhanced peridynamic element to couple non-ordinary state-based peridynamics with finite element method for fracture analysis

Abstract

The non-ordinary state-based peridynamics (NSPD) is a promising method for fracture analysis, and it can incorporate the constitutive relationship of classical continuum mechanics in peridynamics. However, the high computational cost is one of the main reasons limiting its usage. To improve computational efficiency of NSPD, a stability-enhanced peridynamic (PD) element is proposed to couple NSPD with finite element method (FEM), primarily for fracture analysis. Only the areas where cracks may initiate or propagate are solved with the proposed PD element, while the rest of the model is composed of conventional finite elements. The main feature of the proposed PD element is attributed to that the bond interaction does not have to be parallel to the bond direction in NSPD, and the stability of the element is enhanced by introducing the improved hourglass method into the element to restrain the instability due to the zero-energy mode. Based on the equation of motion of NSPD and the principle of virtual work of the PD element, the stiffness matrix of the PD element is derived and the coupled NSPD and FEM method with a global stiffness matrix is thus established. Meanwhile, a two-step interface correction method is developed to improve the accuracy at the interface of the two domains. Subsequently, to verify the proposed coupling method, the uniaxial tension of a strip plate, the propagation of longitudinal wave, the compact tension test of a steel plate, and the single edge notched tension test of an orthotropic lamina are simulated. With the proposed coupling method, the fracture process is accurately simulated, while the computing time is significantly reduced by up to more than 80% when compared with the one using NSPD alone. Moreover, with the constitutive relationship represented by the elastic tensor, the orthotropic materials can be easily modeled in the proposed PD element, and the stress-based criteria can be used with minor modifications. The proposed coupled NSPD and FEM method has high accuracy, computational efficiency, and convenience, and it has the potential to be a useful tool for quantitative analysis of complex engineering fracture problems.