The problem of predicting the growth of a system of cracks, each crack influencing the growth of the others, arises in multiple fields. We develop an analytical framework toward this aim, which we apply to the `En-Passant' family of crack growth problems, in which a pair of initially parallel, offset cracks propagate nontrivially toward each other under far-field opening stress. We utilize boundary integral and perturbation methods of linear elasticity, Linear Elastic Fracture Mechanics, and common crack opening criteria to calculate the first analytical model for curved En-Passant crack paths. The integral system is reduced under a hierarchy of approximations, producing three methods of increasing simplicity for computing crack paths. The last such method is a major highlight of this work, using an asymptotic matching argument to predict crack paths based on superposition of simple, single-crack fields. Within the corresponding limits of the three methods, all three are shown to agree with each other. We provide comparisons to exact results and existing experimental data to verify certain approximation steps.
Why is nacre strong? II: remaining mechanical weakness for cracks propagating along the sheets
在我们以前的论文（Eur。Phys.J.E4，121（2001）），我们提出了用于珍珠层或硬层和软层的分层结构的粗粒弹性能。然后，我们分析了垂直于层的裂纹，并提出了这种物质韧性增强的一个可能原因。在本文中，我们考虑一个平行于层的裂纹。我们提出了一个新的术语添加到以前的弹性能量，这是与层的弯曲。我们发现，有两个制度的平行断裂解决方案的弹性能量;附近的断裂尖端的变形场是由一个抛物型微分方程，而远离尖端的字段遵循通常的椭圆方程。分析结果表明，断裂尖端是透镜状的，正如一篇关于近晶相液晶的论文（P.G. de Gennes，Europhys. Lett. 13（8），709（1990））。相反，远离尖端，应力和变形分布恢复通常的奇异行为（分别为sqrt（x）和1/sqrt（x），其中x是到尖端的距离）。这表明在平行断裂的情况下韧性没有增强。
On the complementary roles of anisotropic crack density and anisotropic crack driving force in phase-field modeling of mixed-mode fracture
School of Mechanical Engineering, Changwon National University（昌原国立大学机械工程学院）；Department of Smart Shipbuilding Systems, Mokpo National University（木浦国立大学智能造船系统系）
