An energy method for calculating the stiffness of aligned short-fiber composites

Abstract A procedure is presented for calculating the longitudinal elastic modulus of a composite possessing dilute concentrations of aligned cylindrical fibers. For a dilute concentration of fibers, the modulus can be written in terms of the perturbation that a single fiber induces in the displacement field of an otherwise homogeneous body subjected to remote uniaxial tension. A boundary value problem, referred to as the auxiliary problem, is formulated which yields the perturbed displacement field directly. The longitudinal modulus can then be expressed in terms of the potential energy of the auxiliary problem; thus, energy-based approximate methods (e.g. FEM) can be exploited to calculate the modulus accurately. With a small modification, this procedure is shown to be applicable to the case of fibers which are imperfectly bonded to the matrix. Moduli for a few representative cases are calculated using a finite element method. Finally, a new means of defining and computing the ineffective length of a fiber is introduced.