This work addresses the scattering of time‐harmonic waves by a finite, blunt nano‐crack in a graded isotropic bulk material with a free surface. The mechanical model is based on classical elastodynamic theory and describes the elastic, isotropic, graded half‐plane with quadratically varying material parameters along the depth coordinate. This model is extended to nano‐mechanics by using non‐classical boundary conditions and localized constitutive equations at the interface between crack and matrix material following the Gurtin‐Murdoch surface elasticity theory. The computational technique employed is based on the non‐hypersingular traction boundary integral equation method (BIEM) using a closed form Green's function for a half‐plane consisting of a functionally graded material (FGM). The dependences of the diffracted and scattered waves and of the local stress concentration fields on key problem parameters such as size and depth of the embedded crack, surface elasticity effects, type and characteristics of the incident wave, and the dynamic interaction phenomenon between the crack and the free‐surface boundary are all examined through parametric studies.

中文翻译：

---

时谐波下梯度纳米裂纹弹性半平面的BIEM分析

这项工作解决了在具有自由表面的梯度各向同性块状材料中有限的钝性纳米裂纹对时间谐波的散射。力学模型基于经典的弹性动力学理论，描述了弹性，各向同性，渐变的半平面，其材料参数沿深度坐标呈二次变化。遵循古尔丁-默多克表面弹性理论，通过使用非经典边界条件和在裂纹与基体材料之间的界面处的局部本构方程，将该模型扩展到纳米力学。所采用的计算技术基于非奇异型牵引力边界积分方程方法（BIEM），该方法对包含功能梯度材料（FGM）的半平面使用闭合形式的格林函数。