含初始裂纹巴西圆盘劈裂问题的非局部近场动力学建模

Nonlocal Peridynamic Modeling for Split of Notched Brazilian Disk

采用近场动力学方法对巴西圆盘劈裂破坏问题进行建模分析.在非局部键型近场动力学(Peridynamics,PD)理论基础上,通过引入物质点对的转动自由度构建双参数微观弹脆性近场动力学本构模型以突破常规模型的应用范围限制,并考虑岩石混凝土类固体材料的宏观拉压异性和断裂特征.引入动态松弛、粒子系统力边界条件和平衡收敛准则等算法,构建了完备的PD求解体系.实现了含不同倾角中心裂纹巴西圆盘受压劈裂破坏全过程的近场动力学数值模拟,裂纹扩展路径及破坏形式均与试验结果高度吻合.进一步分析了初始中心裂纹倾角及其相对长度对巴西圆盘破坏荷载的影响.

The split failure of Brazilian disk has attracted serious concern from researchers in solid mechanics and related engineering fields for measuring the mechanical properties of rock-like materials subjected to tension.Moreover,it is difficult to simulate local damage and crack propagation process using the common numerical methods.The recently developed peridynamic theory provides feasibility to analyze the discontinuous phenomena of materials and structures due to the integral forms of fundamental equations.Inthe present work,aperidynamic（PD）approach is proposed and employed to study the split failure of Brazilian disk.First,the relative rotation of pair-wise bonds is considered in order to solve the limitation of applied range in conventional PD constitutive model,and the mechanical behavior and fracture characteristics of rock-like solid materials are taken into account as well.A complete PD solution system is then developed through introducing a series of physical algorithms including dynamic relaxation,force boundary condition,equilibrium and convergence criterion.The failure process of center-cracked Brazilian disk of different angles is numerically simulated using the presented PD method,and the corresponding result images such as the failure mode and displacement nephogram are obtained.It is found that the numerical crack propagation paths and final failure mode agree well with the experimental observation.It shows that the presented PD method is feasible to investigate the split failure of center-cracked Brazilian disk and offers new research thinking on the tensile failure of rock-like solid materials.The effects of angle and relative length of center cracks on failure load are further simulated and discussed.The correlation curves of failure load-angle of center cracks and failure load-relative length of center cracks are plotted.The results show that both the angle and relative length of center cracks affect the failure load of structure,and size effect exists for the current material and structure.