Failure of Unidirectionally Reinforced Composites with Frictional Matrix

Abstract

A failure criterion for a composite with a frictional matrix and unidirectionally oriented tensile inclusions is presented. The frictional matrix is comprised of granular material with or without cohesion. An energy-based homogenization technique is used to derive the macroscopic stress state associated with the limit state of the composite. The failure condition for a composite with long inclusions is expressed as a piecewise function, and a closed-form representation is given. A numerical scheme is presented for finding the collapse criterion for a composite reinforced with short fibers. Conditions derived can be used, for instance, to describe collapse of reinforced soils. A solution to a boundary value problem is presented, using the method of characteristics for solving the set of hyperbolic-type partial differential equations. A peculiar type of stress discontinuity is found, characteristic of plastic stress fields in anisotropic materials.