Numerical solutions of three dimensional dynamic crack problems and simulation of dynamic fracture phenomena by a “non-standard” finite difference method
Numerical solutions of three dimensional dynamic crack problems and simulation of dynamic fracture phenomena by a “non-standard” finite difference method
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三维动态裂纹问题的数值解以及“非标准”有限差分法模拟动态断裂现象
DOI：
10.1016/0013-7944(78)90028-0
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
Y. Chen
中科院分区：
文献类型：
--
作者：
Y. Chen
简要介绍了非标准有限差分方法（HEMP 和 HEMP 3D 计算机代码）的新颖特征。为了证明 HEMP 3D 代码具有外推子程序解决线性断裂力学动态问题的能力，考虑了施加到内表面的 Heaviside 函数时间相关压力下圆柱管截面的全厚度裂纹和半椭圆表面裂纹，并计算了它们的动态应力强度因子。利用HEMP程序，结合等效自由表面边界条件法和人工速度法，对刚性圆柱冲头刺入线弹性脆性材料圆柱圆片中心引起的动态断裂现象进行了数值模拟。这里选择一个简单的物理模型，即裂纹将在达到临界应力的任何区域中萌生和扩展，并且裂纹将沿垂直于最大主应力的方向扩展。
A brief presentation of the novel features of a non-standard finite difference method (HEMP and HEMP 3D computer codes) is given. To demonstrate the capability of the HEMP 3D code with the extrapolation sub-routine for solving dynamic problems in linear fracture mechanics, through-thc-thickness cracks and semielliptic surface cracks of a section of cylindrical pipe under Heaviside-function time dependence pressure applied to the interior surface are considered and their dynamic stress intensity factors are calculated. The dynamic fracture phenomenon caused by the penetration of a rigid cylindrical punch into the center of a cylindrical wafer of linear-elastic brittle material is simulated numerically by using the HEMP code with the incorporation of the method of equivalent free-surface boundary conditions and the method of artificial velocity. A simple physical model that crack will initiate and propagate in any region where a critical stress has been reached and the crack will propagate in a direction perpendicular to the maximum principal stress is chosen here.