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The motivating key for this work was the absence of a phenomenological model that can reasonably predict a variety of non-proportional experimental data on the anisotropic Mullins effect for different types of rubber-like materials. Hence, in this paper, we propose a purely phenomenological direction dependent orthotropic model that can describe the anisotropic Mullins behaviour with permanent set and, has orthotropic invariants that have a clear physical interpretation. The formulation is based on an orthotropic principal axis theory recently developed for nonlinear elastic problems. A damage function and a direction dependent damage parameter are introduced in the formulation to facilitate the analysis of anisotropic stress softening in rubber-like materials. A direction dependent free energy function, written explicitly in terms of principal stretches, is postulated. The proposed theory is able to predict and compares well with experimental data available in the literature for different types of rubberlike materials. [ABSTRACT FROM AUTHOR]

Abstract: Seven invariants, with immediate physical interpretation, are proposed for the strain energy function of nonlinear orthotropic elastic solids. Three of the seven invariants are the principal stretch ratios and the other four are squares of the dot product between the two preferred directions and two principal directions of the right stretch tensor. A strain energy function, expressed in terms of these invariants, has a symmetrical property almost similar to that of an isotropic elastic solid written in terms of principal stretches. Ground state and stress–strain relations are given. Using principal axes techniques, the formulation is applied, with mathematical simplicity, to several types of deformations. In simple shear, a necessary and sufficient condition is given for Poynting relation and two novel deformation-dependent universal relations are formulated. Using series expansions and the symmetrical property, the proposed general strain energy function is refined to a particular general form. A type of strain energy function, where the ground state constants are written explicitly, is proposed. Some advantages of this type of function are indicated. An experimental advantage is demonstrated by showing a simple triaxial test can vary a single invariant while keeping the remaining invariants fixed. [Copyright &y& Elsevier]