关键词: 常规态型近场动力学, 线性近场动力学固体模型, 含裂纹板模型, 波的传播, 数值模拟, 频散分析

Abstract: Peridynamic theory uses integral form of motion equations, which can effectively avoid the problem that the spatial partial derivative does not exist. It is widely used in simulating discontinuous problems such as crack propagation and fracture damage in different material models. However, there are few studies on wave propagation and dispersion characteristics in peridynamic theory model. In order to study the propagation law of waves in peridynamic theory model, in the case of plane stress, the equations of motion in integral form are established, and the wavefield numerical simulation of isotropic plate model and plate model with parallel cracks are carried out, and the wavefields of longitudinal and shear waves in the classical continuum theory are compared and analyzed. Based on motion equations of ordinary state-based peridynamic theory, the dispersion relations for 1D and 2D are derived in detail. The influences of peridynamic parameters such as the number of material point, the radius of the horizon and the shape parameter on the dispersion curves are comprehensively discussed. In wavefield numerical simulation, the wavefield numerical simulation results of the linear peridynamic solid (LPS) model and the linear elastic solid of the classical continuum theory are in good agreement. The existence of cracks in the model will cause reflection and diffraction of waves during propagation. In the analysis of dispersion characteristics, the dispersion characteristics of LPS model are more consistent with those of the classical continuum model when the  radius of the horizon is smaller and the  shape parameter is larger.

Key words: ordinary state-based peridynamics, linear peridynamic solid model, cracked plate model, wave propagation, numeric simulation, dispersion analysis