Effective transverse response of fiber composites with nonlinear interface

This paper presents a framework for the analysis of the constitutive response of composites in which nonlinear behavior originates solely from the force-separation response of the interfaces. The direct method of composite materials theory is employed to pass from local nonlinear behavior of a solitary inclusion problem to nonlinear aggregate response. The resulting model, which involves no adjustable parameters, falls within the conceptual framework of continuum damage mechanics with "damage" variables that have geometrical meaning on the microscale. They are shown to be the expansion coefficients arising in the eigenfunction representation of the displacement jump at a representative inclusion-matrix interface. Detailed calculations of stress-strain response are carried out for the case of transverse shear and plane dilatation of unidirectional fiber composites in dilute concentration. Bifurcation of equilibrium separation in the solitary inclusion problem is shown to precipitate instability in composite response. Interfaces are assumed smooth and such that normal separations are governed by the nonlinear force law of Ferrante et al. (1982). Comments on the extension of the formulation to include the effects of finite concentration are provided as well.