Analysis of the Antiplane Problem with an Embedded Zero Thickness Layer Described by the Gurtin-Murdoch Model

The antiplane problem of an infinite isotropic elastic medium subjected to a far-field load and containing a zero thickness layer of arbitrary shape described by the Gurtin-Murdoch model is considered. It is shown that, under the antiplane assumptions, the governing equations of the complete Gurtin-Murdoch model are inconsistent for non-zero surface tension. For the case of vanishing surface tension, the analytical integral representations for...