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alumina particles analysis anisotropic approximation axial stress biaxial stiffening binder material boundary conditions boundary value problem composite cylinder composite materials composite strength considered cosh 77 defined deg Figure Effect of Variation effective elastic moduli elastic constants energy density epoxy evaluated experimental fiber end fiber fractures fiber length FIBER RADIUS RATIO fiber region fiber reinforced material fiber strength FIBER VOLUME FRACTION fibrous composites five elastic fractional volume geometry given GROSS FIBER VOLUME Hashin hexagonal array holes Hollow Glass Fibers ineffective length isotropic layer ljkl load longitudinal matrix material Matrix Parallel Fibers Number obtained oriented voids plane strain Plastic Matrix Parallel plate Poisson's ratio present random array reinforced plastic shear modulus shear strain shear stress shear yield stress shown in fig solid fibers solution strain energy stress vectors Stretching Stiffness surface tensile strength test specimens transverse effectiveness Transverse Young's Modulus uniaxially upper bound vanish viscosity