近场动力学理论在脆性材料波散射与裂纹扩展问题的数值模拟

近场动力学(Peridynamic,PD)理论是一个物质点具有通用积分运动方程的连续介质理论,其非局部思想能够很好的处理和解决传统连续介质力学在裂纹尖端解的奇异性问题,也弥补了有限元法(FEM)在断裂问题上网格重构的缺陷,在研究材料的断裂与损伤方面有着独特的优势。基于固体力学和断裂力学理论在应力波传播的研究基础上,通过对比传统波动理论和PD理论中P波的传递速度、传递半径及受载出现的波反射和绕射现象,提出近场力波的概念,从本质上分析了近场力波与应力波传递的区别。用PD理论对含预制缺陷的脆性材料(混凝土)动态断裂过程进行数值模拟,通过分析C15混凝土受冲击载荷断裂过程的能量释放速率得出近场力波的传递会对裂纹的萌生和扩展产生影响。

Numerical Simulation of Wave Scattering and Crack Propagation of Brittle Materials based on Peridynamic Theory

Peridynamics is a continuous medium theory that material points have a general integral vibration equation, whose non-local thought can deal with the singular problem of traditional continuous media mechanics in crack tip solution. In PD theory, the defect of mesh reconstruction when we use the finite element method (FEM) to solve the fracture problem is compensated. There is a unique advantage in studying the fracture and damage of materials when using PD theory. Based on traditional solid mechanics and fracture mechanics in the study of stress wave, we compared and analyzed some characteristics of P wave, such as velocity, transmission radius, wave reflection and diffraction phenomenon. Then the concept of Peridynamic force wave is proposed. Essentially, the difference between Peridynamic force wave and stress wave was analyzed. The numerical simulation of wave scattering during the fracture process of the brittle material(Concrete) with prefabricated defect was implemented and the energy release rate of C15 concrete during fracture process was analyzed, and we found the transmission of Peridynamic force wave can affect the crack initiation and propagation.