  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.
