Robust numerical analysis of homogeneous and non-homogeneous deformations

The present paper is devoted to the modeling of finite deformations of hyperelastic bodies described by Ogden's model. For the finite element implementation, the explicit expressions of the tangent operator and the stress tensor are derived. If the eigenvalues of the right Cauchy–Green strain tensor are distinct, a simple and compact tensor formula, well adapted for numerical implementation, is proposed. A limiting technique is used to take into account the special case of coalescent eigenvalues in which non-differentiability occurs. Three test examples, including homogeneous and non-homogeneous deformations, are proposed to illustrate the developed formulation.