A symmetric constitutive matrix for the non‐linear analysis of hypoelastic solids based on a formulation leading to a non‐symmetric stiffness matrix

The aim of this paper is to implement and to apply a mathematical model to analyse solid mechanics problems involving non-linear hypoelastic isotropic or orthotropic materials using the finite element method. An updated Lagrangian description with a corotated Kirchhoff stress tensor was taken on. This description leads to a non-symmetric stiffness matrix. An alternative, using a symmetric constitutive matrix is addressed and some of its main mathematical and numerical characteristics are highlighted. Numerical examples for simple systems were solved and good results were obtained using a symmetric constitutive matrix, although average relative errors increase with the influence of shear stress effects. Important saving in processing time and computer memory may be obtained if a symmetric constitutive matrix is used. Copyright © 2007 John Wiley & Sons, Ltd.

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