Orthotropic and transversely isotropic stress-strain relations with built-in coordinate transformations

Abstract

Computationally convenient elastic stress-strain relations are given for orthotropic and transversely isotropic materials in terms of unit vectors that are aligned in the preferred material directions. Methods are proposed for determining the material symmetry planes from mechanical and thermal response. The restrictions on the elastic constants that are discussed by Jones (1975) are specialized to the case of transverse isotropy. It is shown that the laminated composite structures with high in-plane stiffness may easily violate these restrictions. The incompressible version of the stress-strain relations are presented for materials that do not deform under hydrostatic loading. This version applies to composite structures made with incompressible epoxy matrices and stiff fibers. For incompressible laminated structures the restrictions on the elastic constants are violated when the in-plane modulus ET and the out-of-plane modulus EA are governed by ET > 4EA. Violation of the restrictions may be the cause of the common occurrence of interlaminar shear failure and edge delamination. In order to avoid excessive load transfer, it may be beneficial to keep the fiber matrix Young's moduli in the range Ef < 20 Em.