Cosserat interphase models for elasticity with application to the interphase bonding a spherical inclusion to an infinite matrix

Interphases are often modeled as interfaces with zero thickness using jump conditions that can be developed based on approximate shell or membrane models which are valid for specific limited ranges of the elastic material parameters. For a two-dimensional problem it has been shown (Rubin and Benveniste, 2004) that the Cosserat model of a finite thickness interphase is a unified model that is accurate over the full range of elastic parameters. In contrast, many other interphase models are valid for only limited ranges of the elastic parameters. In this paper, the accuracy of different Cosserat models of a finite thickness interphase that connects a spherical inclusion to an infinite matrix is examined. Specifically, four Cosserat interphase models are considered: a general shell ( GS ) , a membrane-like shell ( MS ) , a simple shell ( SS ) and a generalized membrane ( GM ) . The models ( GS ) and ( MS ) both satisfy restrictions on the strain energy function of the interphase that ensure exact solutions for all homogeneous three-dimensional deformations, while the other models ( SS ) and ( GM ) do not satisfy these restrictions. The importance of these restrictions is examined for the three-dimensional inhomogeneous inclusion problem being considered. This is the first test of the accuracy of an elastic interphase model for a spherical interphase.