基于近场动力学理论的裂纹模型波场数值模拟及频散特性分析

Numerical Simulation and Dispersion Characteristics Analysis of Crack Model Wavefield Based on Peridynamic Theory

近场动力学理论采用积分形式的运动方程,能够有效避免空间偏导数不存在的问题,在模拟不同材料发生裂纹扩展、断裂破坏等不连续问题方面有着广泛应用,但是对近场动力学理论中波的传播问题和频散特性研究较少。为了研究近场动力学理论中应力波的传播规律,考虑平面应力情况,建立积分形式的运动方程,在均匀各向同性模型及含水平裂纹模型下进行了波场数值模拟,并与经典连续介质理论中的纵波和横波波场进行对比分析。基于常规态型近场动力学理论的运动方程,详细推导了一维和二维情况下的频散关系,并探讨了邻域内物质点数、邻域半径和形状参数等近场动力学参数对频散曲线的影响。在波场数值模拟中,线性近场动力学理论中固体与经典连续介质理论中线弹性介质的波场数值模拟结果具有良好的一致性,介质内裂纹的存在会阻碍波的传播;在频散特性分析中,所选邻域半径越小、形状参数越大,线性近场动力学理论中的频散特性越接近经典连续介质力学理论中的频散特性。

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.