GENERALIZED CONTINUUM THEORIES FOR DIRECTIONALLY REINFORCED SOLIDS.

A theory of elasticity with microstructure for fiber reinforced composites with a rectangular array of the fibers is outlined. The theory is based on expansions of the displacements across representative cells. The transition from the actually inhomogeneous composite to a homogeneous continuum is achieved by introducing continuous fields for gross displacements and local deformations. The elastic constants are expressed explicitly in terms of the constants defining the mechanical behavior of the fibers and the matrix material, and the parameters describing the geometrical layout of the composite. A number of specific examples involving the dispersive behavior of time-harmonic waves propagating in directions parallel and normal to the fibers are discussed. These cases are relevant to available data of ultrasonic tests on composite materials. Anayltical results are compared with test data, and with some results obtained by the finite element technique.