Two-dimensional DtN-FEM scattering analysis of SH guided waves by an interface debonding in a double-layered plate

TL;DR

This paper introduces a 2D DtN-FEM approach for analyzing SH guided wave scattering caused by interface delamination in bi-material plates, offering advantages in dimension reduction and direct mode coefficient extraction.

Contribution

The paper develops a novel 2D DtN-FEM method that simplifies scattering analysis of guided waves without needing absorption layers or PMLs, and allows direct calculation of mode coefficients.

Findings

Accurately models wave scattering at interfaces in bi-material plates.

Provides a dimension-reduced method with no need for absorbing layers.

Enables direct computation of reflection and transmission coefficients.

Abstract

In this paper, a two-dimensional Dirichlet-to-Neumann (DtN) finite element method (FEM) is developed to analyze the scattering of SH guided waves due to an interface delamination in a bi-material plate. During the finite element analysis, it is necessary to determine the far-field DtN conditions at virtual boundaries where both displacements and tractions are unknown. In this study, firstly, the scattered waves at the virtual boundaries are represented by a superposition of guided waves with unknown scattered coefficients. Secondly, utilizing the mode orthogonality, the unknown tractions at virtual boundaries are expressed in terms of the unknown scattered displacements at virtual boundaries via scattered coefficients. Thirdly, this relationship at virtual boundaries can be finally assembled into the global DtN-FEM matrix to solve the problem. This method is simple and elegant, which has advantages on dimension reduction and needs no absorption medium or perfectly matched layer to suppress the reflected waves compared to traditional FEM. Furthermore, the reflection and transmission coefficients of each guided mode can be directly obtained without post-processing. This proposed DtN-FEM will be compared with boundary element method (BEM), and finally validated for several benchmark problems.