PERIDYNAMIC METHOD BASED ON NONLOCAL LSM OPTIMIZATION AND DEFORMATION SIMULATION OF BRITTLE MATERIALS

Based on the peridynamic model, the relationship between the micro modulus in peridynamics and the elastic constants in classical theory is established by assuming small deformation. The kernel function which can reflect the nonlocal action characteristics is introduced to improve the calculation accuracy, and the linear equations related to the micro modulus are established by means of stiffness equivalence. The least square minimum (LSM) norm solution of uncertain linear equations is used to optimize the micro modulus in peridynamics, and the optimal nonnegative modulus is obtained through quadratic programming. The deformation of two-dimensional plate under uniaxial and biaxial loads and the crack growth of brittle material with prefabricated cracks under loads are simulated by the optimized method, and the results are compared with those by classical peridynamics method. The results show that the optimized method can better reflect the deformation and failure characteristics of the structure under load conditions, and the maximum error and error range of material deformation simulation are better than the classical method; and moreover, the simulation of crack growth process has better convergence speed and convergence results under the same calculation cost, which verifies the effectiveness and the wide application prospect of the proposed method.