A nonlinear Cosserat interphase model for residual stresses in an inclusion and the interphase that bonds it to an infinite matrix

Residual stresses in inclusions and interphases that are bonded to a matrix can significantly influence the response of composite materials to additional mechanical loads. These residual stresses are modeled by considering the nonlinear 2-phase problem of an inclusion that is bonded to a hollow spherical interphase with an internal unstressed radius that is different from the outer unstressed radius of the inclusion and with a traction-free outer deformed surface. The resulting macro-inclusion (i.e. the prestressed inclusion and interphase) is then embedded into a stress-free matrix. The linear equations for small deformations superimposed on this large deformation problem are developed and solved to study the influence of the residual stresses on the response of the 3-phase system of inclusion-interphase-matrix to external mechanical loads. The results of this solution indicate that this residual stress problem is essentially nonlinear and must be modeled directly by including the influence of coupled terms associated with products of the residual stresses and displacements.