Analysis of viscoelastic behaviour of transversely isotropic materials

In this paper a constitutive equation to describe the mechanical behaviour of materials, reinforced with unidirectional fibres, is presented. The material behaviour of both matrix and fibres may be viscoelastic. The constitutive equation is a linear relation between the second Piola–Kirchhoff stress tensor and the Green–Lagrange strain tensor. The effective relaxation functions in the constitutive equation are composed of component relaxation functions employing the structural model of Hashin and Rosen. A two-dimensional membrane element incorporating this constitutive equation is implemented in a finite element program. The results of several calculations are presented in order to demonstrate the possibilities of the numerical tool. One calculation concerns a square membrane with a circular hole in its centre. The effect of fibre orientation on deformation and stresses will be displayed for this structure as well as for another membrane structure.