Higher-order nonlocal operator theory for phase-field modeling of ductile fracture in elasto-plastic materials

In this work, we propose a novel approach based on the higher-order nonlocal operator for the phase-field modeling of ductile fracture in elasto-plastic materials. The present method introduces the total energy function consisting of the elastic, plastic, and fracture terms. The plasticity is coupled with the fracture through the degradation function which is applied to the tensile part of the elastic strain energy. The proposed higher-order nonlocal operator method brings several advantages over the original nonlocal operator method that requires only first-order terms. Moreover, the proposed method does not require the direct computation of kernel function or moment matrix derivatives. Therefore, this approach can improve the computational efficiency and simplify in implementation. The accuracy and effectiveness of the proposed method are demonstrated through various numerical examples, which have the ability to detect complex patterns of ductile fracture, such as crack propagation and plastic localization.