Nonlinear behavior of wavy composites under tension

Abstract

A composite structure consisting of doubly periodic moderately wavy layers under tension is considered. The periodic cell of the composite is represented by two layers of different materials, but having the same arbitrary initial shape. As opposed to theories with full homogenization, the thickness of the periodic cell with respect to its length is not assumed to approach zero in the analysis. The influence of this structural parameter is shown to be especially significant if the material of one of the layers is much weaker than the other. Using a geometrical nonlinear Cosserat rod model to describe the layers, we take into account extension flexure and shear deformation in the layers. The problem is reduced to a boundary value problem for a scalar nonlinear ODE of second order for the rotational degree of freedom. The determination of the deformed shape of the layers, as well as the relation between the elongation of the periodic cell and the applied tension force is then reduced to nonlinear quadratures. For the case of small initial waviness, an analytical solution is obtained for an arbitrary initial shape of the layers. For moderate initial waviness numerical results are presented relating stress, strain and amplitude of waviness. The influence of material and structural parameters is investigated and discussed.