The fiber composite with nonlinear interface—part ii: Antiplane shear

This paper treats the effective antiplane shear response of a composite consisting of fibers that interact with the matrix through nonlinear Needleman-type cohesive zones. The first paper (Part I) examines effective axial tension response. The composite cylinders repre- sentation of a representative volume element (RVE) is employed throughout. For anti- plane shear loading the elastic field solution for a single composite cylinder is found in the form of a series expansion whose coefficients are governed by an infinite set of nonlinear equations. Bounds on the total potential energy and the total complementary energy/of an RVE do not coincide although they' are shown to differ by a term of order 0(c4) where c is the fiber volume concentration. Interaction effects due to finite volume concentration, coupled with nonlinear interface characterization, are shown to precipi- tate instability in composite response.