The shear modulus of a composite material with a transversely isotropic matrix and a fibre

A relation is proposed for determining of the shear modulus of a fibrous composite material with a transversely isotropic matrix and a fibre as a function of the elastic constants of the matrix and the fibre as well as the volume fraction of each of them in the composite material. The isotropy planes of the matrix and fibre coincide and are perpendicular to the fibre axis. Two boundary value problems are solved in order to obtain the required relation: the problem of the longitudinal shear of a transversely isotropic solid cylinder that simulates the fibrous composite material and the problem of the combined longitudinal shear of a hollow and solid cylinder that simulate the matrix material and the fibre material respectively. Calculations using the proposed formula are compared with the available experimental data.