Finite Element analysis of the wrinkling of orthotropic membranes

This work presents a fully nonlinear formulation for the analysis of the wrinkling on orthotropic membranes. Our approach describes the membrane kinematics as a thin shell motion, whose bending stiffness comes naturally from the shell assumptions. We combine the geometrically-exact isotropic shell model of [

1

],[

2

] with an orthotropic constitutive equation for the membrane strains (see [

3

],[

4

]), so that both bending and typical membrane capabilities are present in a totally consistent way. The strain energy function is split into an isotropic and an orthotropic part, the first one being relative to the shell (hyperelastic) behavior and the latter to the membrane deformations. The model is discretized under the light of the finite element method using the six-node triangular element of [

2

], and the performance of the formulation is assessed in several numerical examples (see e.g. Fig. 1). Unstructured meshes are deliberately employed whereas small geometrical imperfections are imposed for the wrinkles to be initiated. Experimental data from the membrane tests of [

5

] are also taken into account for comparison with our results.

Fig. 1

Stretching of two orthotrophic membranes. Deformed configurations.