Time-harmonic SH-wave scattering by a nanocrack in a continuously inhomogeneous magnetoelectroelastic (MEE) plane with exponentially dependent material parameters and under conditions of anti-plane strain is studied. A non-hypersingular, traction-based boundary integral equation method (BIEM) for solution of the problem under consideration is presented. The BIEM formulation combines classical elastodynamic theory for the graded bulk MEE solid with non-classical boundary conditions and the localized constitutive law for the MEE matrix–nanocrack interface within the framework of the Gurtin–Murdoch theory. The presented parametric study reveals the degree of dependence of the dynamic fracture characteristics on the size of the nanocrack, surface and bulk material properties, coupled nature of the magnetoeletroelasticity, properties of the incident wave as frequency, wave length and wave propagation direction, dynamic interaction between the nanocrack, incident wave and coupled magneto-electro-elastic graded continuum.

研究了纳米裂纹在连续非均匀磁电弹性（MEE）平面中具有指数依赖的材料参数并且在反平面应变条件下的时谐SH波散射。提出了一种非双曲基于牵引力的边界积分方程法（BIEM），用于解决所考虑的问题。BIEM公式结合了古德汀-默多克理论框架内用于分级体MEE固体的经典弹性动力学理论和非经典边界条件，以及用于MEE矩阵-纳米裂纹界面的局部本构律。提出的参数研究揭示了动态断裂特性对纳米裂纹尺寸，表面和块状材料特性，磁电弹性耦合特性的依赖程度，