PERIDYNAMICS AND NUMERICAL SIMULATION OF SOLID MATERIAL STRESS BASED ON NONLOCAL DIFFERENTIAL OPERATOR

Based on the classical peridynamic model, the nonlocal differential operator solution theory is introduced to establish the peridynamic micro-elastic stress analysis model. Taylor series expansion is carried out at the material point of the peridynamic model. The numerical integral equation of the differential operator is constructed by using the orthogonal nonlocal function, and the unknown coefficients of the function are solved according to the orthogonality of the matrix. Finally, the peridynamic stress solution model is established by the equivalence of the equilibrium equation. The proposed method is used to simulate the stress distribution in the deformation and failure process of solid materials, and the calculated results are compared with the theoretical solution to verify the effectiveness of the method proposed. At the same time, the numerical convergence of the particle discrete distance, Taylor term number and the weight function are analyzed. The simulation results show that the proposed method can accurately reflect the stress distribution of holonomic and nonholonomic solid brittle materials under loads. Moreover, the discrete distance and weight function have a significant influence on the numerical convergence. It can provide a new idea for stress analysis when using the extended peridynamics method to simulate deformation and failure and, has a wide application prospect.