THE INTERIOR ELASTIC STRESS FIELD IN A CONTINUOUS, CLOSE-PACKED FILAMENTARY COMPOSITE MATERIAL UNDER UNIAXIAL TENSION

摘要

Using symmetry arguments, boundary conditions are established which must hold on the lines of symmetry between neighboring filaments in an oriented filamentary composite. These conditions serve to set the problem as a special case of the mixed boundary value problem of elasticity.nThe composite is assumed to deform such that the normal strains in the direction of the filament axes are the same in both media. The equations of elasticity are then solved in polar coordinates so that the solution has the appropriate sixfold symmetry. Because boundary and continuity conditions must be described on both a straight and circular boundary, the solution is not in closed form. The in-plane stresses vanish when the Poisson's ratios of the two media are identical.