Imperfect soft and stiff interfaces in two-dimensional elasticity

A thin curved isotropic layer of constant thickness between two elastic isotropic media in a two-dimensional plane strain setting is considered. The properties of the curved layer are allowed to vary in the tangential direction. We aim at modeling this layer by an interface between the two media across which certain conditions on the tractions and displacements will prevail. It is shown that depending on the softness or stiffness of the layer with respect to the neighboring media, there exist seven distinct regimes of interface conditions. Two of these conditions describe the case of a layer which is soft with respect to the neighboring media; they will be referred to as "soft interface" conditions. One condition describes ideal contact. The remaining four, called "stiff interfaces", concern the case of a stiff interphase. The stiff interface conditions which bear a close resemblance to membrane and classical shell theories are new and constitute the main contribution of this work. The derivation is based on the use of an asymptotic expansion for the elastic field in the layer.