Orthotropic swelling and simplified elasticity laws with special reference to cord-reinforced rubber

Abstract

Further implications of equations for the directional dependence of swelling (1) and elastic modulus (2) which were originated by Coran, Boustany, and Hamed1 are given. Equation (1) is practically equivalent to the standard tensor transformation equation assuming that swelling is equivalent to negative hydrostatic pressure and the new relationship is derived for the case E1 ≫ E2. A corollary of eq. (1), (3) conflicts with three commonly used models of unidirectional composites. Anisotropic laminate theory is used to show that eq. (3) has important consequences for multiply laminates with no triangulation. These results indicate that the equations of Coran et al. cannot be expected to have wide application to other systems, especially continuous cord-reinforced rubber.