The Ghost Solid Methods for the Solid-Solid Interface

Abstract

Original and modified variants of the Ghost Solid Method (GSM) are proposed for application to the boundary conditions at the solid-solid interface of isotropic linearly elastic, as well as elastic-plastic materials, in a Lagrangian framework. The methods are discussed for one dimensional as well as two dimensional settings with slip and no-slip conditions. The effect of using different solvers for these methods is discussed. It is shown, in the presence of the wave propagation through the solid-solid mediums, the original GSM can lead to large numerical errors in the solution, either in the form of large oscillations in stress and velocity at the interface, or significant deviations from the exact solution. A scheme for prediction of these errors at the interface is also introduced. The other two variants of GSM proposed, however, can remove the large numerical errors that may rise at the interface. Numerous numerical examples in one and two-dimensional settings are provided attesting to the viability and effectiveness of the GSM for treating wave propagation at the solid-solid interface.