Wavefield analysis of nano-scale surface/interface effects on dynamic stress response in biphasic laminated media with circular defects

Abstract

The dynamic stress concentration around a nanoscale circular hole located at the centre of a two-phase circular laminated medium subjected to localized anti-plane SH-wave loading is examined in this paper. The model (used in this paper) is developed using the complex variable function method combined with wavefield superposition and multipolar expansion. In this framework, Gurtin–Murdoch (GM) surface and interface elasticity is incorporated at both the material interface and the free surface of the nanohole, resulting in a coupled two-surface formulation that has not been previously reported for biphasic geometries. This leads to non-classical traction-jump conditions and modified stress-free boundary conditions. The resulting infinite system of linear equations is then solved through series truncation. Numerical results reveal that nanoscale surface and interface effects significantly reduce the dynamic stress concentration factor (DSCF) around the hole, with the most substantial attenuation occurring at low wavenumber ratios and low shear modulus ratios. Conversely, the stress reaches its maximum amplification under long-wavelength excitation or when the outer layer is relatively soft. Overall, these findings offer new insights into nanoscale toughening mechanisms in realistic multilayered systems, providing a solid foundation for defect detection, lifetime prediction, and the damage-tolerant design of laminated nanocomposites and core–shell nanostructures.