Crystalline materials deform by a process of crystalline slip, whereby material is transported via shear across distinct crystal planes and only in certain distinct crystallographic directions in those planes. This process imparts a strong directionality to the plastic flow process and specifies a clear kinematic definition to the plastic spin. In what follows the theory is developed around a model for a laminated material; this is done to demonstrate the generality of the approach to a broader range of materials where slip is kinematically mediated by fixed directions.

Laminate Model

We consider the fiber reinforced plastic (FRP) material to be composed of an essentially orthotropic laminate, which contains a sufficient number of plies so that homogenization is a reasonable way to describe the material behavior. The principal directions of the fibers are described by a set of mutually orthogonal unit base vectors, ai, as depicted in Fig. 31.1. The resulting orthotropic elastic response of the laminated composite will thus be fixed on and described by these vectors. The material can also deform via slipping in the plane of the laminate, i.e., via interlaminar shear, and this slipping is confined to the interlaminar plane. Slipping is possible in all directions in the plane, but not necessarily with equal ease. We thus introduce two slip systems, aligned with the slip directionss1 and s2. The normal to the laminate plane is m, so that s1 · m = 0 and s2 · m = 0.