FINITE-ELEMENT FORMULATION OF THE OGDEN MATERIAL MODEL WITH APPLICATION TO RUBBER-LIKE SHELLS

The present contribution proposes a variational procedure for the nume rical implementation of the Ogden material model. For this purpose the strain energy density originally formulated in terms of the principal stretches is transformed as variational quantities into the invariant s of the right Cauchy-Green tensor. This formulation holds for arbitra ry three-dimensional deformations and requires neither solving eigenva lue problems nor co-ordinate system transformations. Particular attent ion is given to the consideration of special cases with coinciding eig envalues. For the analysis of rubber-like shells this material model i s then coupled with a six parametric shells kinematics able to deal wi th large strains and finite rotations. The Incompressibility condition is considered in the strain energy, but it is additionally used as 2- D constraint for the elimination of the stretching parameter at the el ement level. A four node isoparametric finite element is developed by interpolating the transverse shear strains according to assumed strain concept. Finally, examples are given permitting to discuss the capabi lity of the finite element model developed concerning various aspects. (C) 1998 John Wiley & Sons, Ltd.