The paper presents the Isogeometric Boundary Element Method (IGABEM) algorithm for solving the plane strain problem of an isotropic linearly elastic matrix containing an open material surface of arbitrary shape. Theoretical developments are based on the use of the Gurtin-Murdoch model of material surfaces. The governing equations and the boundary conditions for the problem are reviewed, and analytical integral representations for the elastic fields everywhere in the material system are presented in terms of unknown traction jumps across the surface. To find the jumps, the problem is reduced to a system of singular boundary integral equations in terms of two unknown scalar components of the surface stress tensor. The system is solved numerically using the developed IGABEM algorithm in which NURBS are used to approximate the unknowns. The main steps of the algorithm are discussed and convergence studies are performed. The algorithm is validated using two benchmark problems involving the matrix subjected to a uniform far-field load and containing a surface along (i) a straight segment and (ii) a circular arc. Numerical examples are presented to illustrate the influence of governing parameters with a focus on the influence of curvature variation.

翻译：本文提出了一种等几何边界元法（IGABEM）算法，用于求解包含任意形状开放材料表面的各向同性线弹性基体的平面应变问题。理论推导基于Gurtin-Murdoch材料表面模型。文中回顾了该问题的控制方程与边界条件，并以材料表面未知牵引力跃变量为参数，给出了整个材料系统内弹性场的解析积分表达式。为求解跃变量，该问题被简化为以表面应力张量的两个未知标量分量为变量的奇异边界积分方程组。该方程组采用本文开发的IGABEM算法进行数值求解，其中使用NURBS对未知量进行近似。文中讨论了算法的主要步骤并进行了收敛性研究。通过两个基准问题验证了算法的有效性：基体承受均匀远场载荷，并分别包含（i）直线段和（ii）圆弧形材料表面。数值算例展示了控制参数的影响，重点分析了曲率变化的作用。