SIAM Journal on Applied Mathematics, Volume 80, Issue 5, Page 2098-2119, January 2020.
This paper considers the problem of interaction of multiple straight plane cracks in the presence of the Steigmann--Ogden surface energy on the crack boundaries. The general boundary conditions with the Steigmann--Ogden surface elasticity are derived in the arc length parametrization of the crack boundary for arbitrary smooth crack geometry. The plane stress problem of linear elasticity for a plate with multiple straight cracks is solved by using integral representations of complex potentials. The resulting system of singular integro-differential equations is reduced to a system of Fredholm equations of the second kind. The existence and uniqueness of the solution are discussed. The numerical results are presented for two straight cracks located on the same straight line. The results are compared to the results of the classical problem for a plate with multiple cracks in the absence of the Steigmann--Ogden energy and to the results for a single straight crack in the plate with the Steigmann--Ogden surface energy on the boundary.

中文翻译：

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Steigmann-Ogden表面能的作用下多平面直缝的相互作用

SIAM应用数学杂志，第80卷，第5期，第2098-2119页，2020年1月。
本文考虑了在裂纹边界处存在Steigmann-Ogden表面能的情况下多个直平面裂纹相互作用的问题。Steigmann-Ogden表面弹性的一般边界条件是在任意光滑裂纹几何形状的裂纹边界的弧长参数化中得出的。通过使用复势的积分表示，解决了具有多个直裂纹的板的线性弹性的平面应力问题。所得的奇异积分微分方程组简化为第二类Fredholm方程组。讨论了该解决方案的存在性和唯一性。给出了位于同一直线上的两个直裂纹的数值结果。