主裂纹与微裂纹相互作用问题的有效数值计算方法

提出了平面弹性介质中主裂纹与微裂纹相互作用问题的有效数值计算 方法. 通过把适于单一裂纹的Bueckner原理扩充到含有多裂纹的一般体系，将原问题分解 为承受远处载荷不含裂纹的均匀问题，和在远处不承受载荷但在裂纹面上承受面力的多裂纹 问题. 于是，以应力强度因子作为参量的问题可以通过考虑后者(多裂纹问题)来解决，而 利用提出的杂交位移不连续法，这种多裂纹问题是容易数值求解的. 列举 Cai和 Faber为评价主裂纹与微裂纹相互作用问题的近似方法而列举的算例，说明 该数值方法对分析平面弹性介质中主裂纹与微裂纹相互作用问题既简单又非常有效.

An effective numerical approach for interaction of macrocrack with mircocracks

In this paper, an effective numerical approach for interaction of macrocrack with microcracks in plane elastic media is presented. By extending Bueckner's principle suited for a single crack to a general system containing multiple interacting cracks, the original problem is divided into a homogeneous problem (the one without cracks) subjected to remote loads and a multiple-crack problem in an unloaded body with applied tractions on the crack surfaces. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by taking into account the latter problem, which is analyzed easily by means of the Hybrid Displacement Discontinuity Method proposed recently by the author. The examples given by Cai and Faber (see, Cai H, and Faber KT. 1992, On the use of approximate methods for microcrack shielding, ASME J. Appl Mech 59, 497-501) for the interaction of a macrocrack with microcracks are exemplified here. It is found that the present approximation method is very simple and effective for microcrack shielding problems.