Constitutive equations for micropolar hyper-elastic materials

In this paper, the concept of hyper-elasticity in the micropolar continuum theory is investigated. The restrictions on the fourth-order elasticity tensors are investigated. Using the representation theorems, a general form of constitutive equations for micropolar hyper-elastic isotropic materials is presented. As some special cases, generalizations of the neo-Hookean and Mooney-Rivlin type materials to the micropolar continuum theory are presented. The generalized constitutive equations reduce to those of the microplar linear elasticity theory when the deformations are infinitesimal. Also, Updated Lagrangian finite element formulations for the micropolar hyper-elastic materials are presented. Considering two planar examples, it is shown that an increase in the micropolar parameter results in the reduction of the deformation of the bodies. Also, it is shown that for a specimen with very small dimensions, e.g. in the micron level, the micropolar effects are more sensible. Furthermore, it is shown that the influence of the micropolar parameters is dependent not only on the size of the body, but also to its geometry and loading conditions. For the problems in which the deformation is very close to a homogeneous state, the micropolar effects are negligible.