The ghost solid methods for the elastic-plastic solid-solid interface and the θ-criterion

Two variants of the Ghost Solid Method (GSM), namely the Original GSM (OGSM) and Modified GSM (MGSM), are proposed for the elastic-plastic solid-solid interactions in a Lagrangian framework. It is shown that the OGSM is highly problem related and can lead to large numerical errors under certain material combinations or in the presence of the wave propagation through the solid-solid interface. The theta-criterion, previously developed for the elastic-elastic solid-solid interactions [1], has been applied to the OGSM for the elastic-plastic interactions. It is shown that this criterion can successfully detect the onset of these large errors. Moreover, it is shown that it can be used to determine the reliability of the results obtained using the OGSM. The MGSM has been shown to be able to remove the large numerical errors that would normally arise due to the OGSM. Next, the extension of the two variants of the GSM, to two-dimensional settings, is presented for two idealized interface conditions, namely the no-slip condition, and the perfect-slip conditions. Numerous numerical experiments are provided attesting to the effectiveness and viability of the GSMs, for simulating wave propagation at the elastic-plastic solid-solid interface. The applicability of the theta-criterion is also studied in the numerical experiments. (C) 2015 Elsevier Inc. All rights reserved.