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

• Published in: Communications in numerical methods in engineering 2008-11, Vol.24 (11), p.1079-1092
• Main Authors: Di Rado, H. A., Mroginski, J. L., Beneyto, P. A., Awruch, A. M.
• Format: Article
• Language: English
• Subjects: anisotropic materials; Computational techniques; corotated formulation; Exact sciences and technology; finite elements; Fundamental areas of phenomenology (including applications); geometrically non-linear analysis; hypoelastic solids; Mathematical methods in physics; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics
• ISSN: 1069-8299; 1099-0887
• DOI: 10.1002/cnm.1015

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.