nonlinear description of fibre-reinforced elastic materials

The constitutive relationships proposed elsewhere Jemioło et al. (1990) are here generalized and discussed in more detail. Nonlinear elasticity equations are considered and modified in such a manner as to suitably describe a composite consisting of an isotropic matrix reinforced with three orthogonal curvilinear families of fibres, each having different mechanical properties. As an alternative, a canonical form of the equations is also formulated. Isotropy, transversal isotropy and local orthotropy are considered as three important practical situations. In each case the reinforcement is described by a positive-valued second order tensor. In addition, the constitutive relationships are derived for such specific situations as plane stress, plane strain and antiplane stress. Two variants of simplified physical relations for linear elasticity are given and compared against the standard Hooke's law. Relations are given enabling material constants to be found with the use of standard tests for orthotropic material.