The Fiber Composite With Nonlinear Interface—Part II: Antiplane Shear

Abstract

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 representation of a representative volume element (RVE) is employed throughout. For antiplane 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 O(c4) where c is the fiber volume concentration. Interaction effects due to finite volume concentration, coupled with nonlinear interface characterization, are shown to precipitate instability in composite response. [S0021-8936(00)02104-8]