非均匀材料破坏过程数值模拟的边界元法研究

用格子模型和统计分布模拟非均匀材料性质的初始分布,针对二维非均匀材料格子模型建立了重复多子域边界元法求解方程。通过把各行子域集成为亚子域,然后对链状排列的亚子域应用域转移矩阵法进行求解。由于使用的域转移矩阵法对内存的要求仅略大于一个亚子域的求解,以及重复多子域法只需要进行一次系数矩阵积分,因而可以大大提高求解的规模和效率。在此基础上,对非均匀脆性材料在简单载荷作用下的破坏过程进行了数值模拟。采用重复多子域法和域转移矩阵法,可以得到子域内高精度的连续应力分布,为进一步研究非均匀材料裂纹萌生、扩展和破坏过程提供了基础。

BEM FOR NUMERICAL SIMULATION OF FAILURE PROCESS IN HETROGENEOUS MATERIALS

In this paper, the lattice model and statistical distributions are used to represent the initial heterogeneous distribution of material properties. Equations of the reduplicate multi-sub-region (RMSR) boundary element method are established for the lattice model of 2-D heterogeneous materials. Each row of sub-regions in the lattice are integrated into a super-sub-region and the transfer matrix of sub-region method (TMSRM) is employed to solve the super-sub-region placed in chain. Since the memory demand of the TMSRM is only a little more than that of solving one super-sub-region and the coefficient matrices are only generated just once in RMSR, the capacity and efficiency can be increased significantly. As an example of application of the above-proposed methods, the failure process of 2-D heterogeneous materials is numerically simulated. With the RMSR and TMSRM, the continuous distribution of stress with high accuracy is expected, which provides a good foundation for further research on the initiation, propagation of crack and failure process in heterogeneous materials.