TANGENT MODULUS MATRIX FOR FINITE-ELEMENT ANALYSIS OF HYPERELASTIC MATERIALS

In this study, using the VEC operator [1], compact expressions are for mulated for the tangent modulus matrix of hyperelastic materials, in p articular elastomers, using Lagrangian coordinates. Compressible, inco mpressible, and near-compressible materials are considered. Expression s are obtained for the corresponding finite element tangent stiffness matrices. It is observed that the incremental stress-strain relations should be considered anisotropic. Numerical procedures based on Newton iteration are sketched. The limiting case of small strain is develope d. Finally, the tangent modulus matrix is presented for the Mooney-Riv lin material, with application to the rubber rod element.