ABSTRACT
Composites structures with elastomeric matrix are widely used by industry. A refined numerical simulation of these structures is mostly needed. This chapter presents a model reduction method, to find the equilibrium state of geometrically complex structures which have invariant properties in a direction. Based on finite-elements formulation, it consists in the projection of the unknown fields on a polynomial basis in order to reduce the dimension of the problem and the model size. The main idea is to make finite element based on higher order shape function to approximate the behavior of an elementary unit of the structure in a direction. The global and local behavior of the reduced models are both examined for the validation. Two applications are shown, a plane strain laminated rubber bearing and a fiber reinforced elastomeric beam. Furthermore, this method is not restricted to hyperelastic law, in fact the gain of material resources, can be used to develop more complicated material laws.
