Mean field estimates of the response of fiber composites with nonlinear interface

This paper presents a theory of the effective response of composites containing general, nonlinearly separating inclusion–matrix interfaces. The direct method of composite materials theory is utilized to pass from local nonlinear behavior of a solitary inclusion problem to nonlinear aggregate response. Interaction effects at finite volume concentration are captured in the representative solitary problem by employing the Mori–Tanaka mean field estimate. The resulting model falls within the conceptual framework of continuum damage mechanics in that nonlinear effective response depends on internal variables that are governed by local evolution equations. The damage variables turn out to be the expansion coefficients arising in an eigenfunction representation of the displacement jump at a representative inclusion–matrix interface. Interfaces are generally modeled according to a nonlinear force-separation law that allows for both normal and shear decohesion (X-.P. Xu, A. Needleman, Modell. Simul. Mater. Sci. Eng. 1 (1993) 111). Detailed calculations of effective stress–strain response are carried out for the case of transverse shear and plane dilatation of unidirectional fiber composites at various values of concentration and interface constitutive constants. The effects of the various parameters on bifurcation of equilibrium separation in the solitary inclusion problem and on overall composite stability are demonstrated as well.