A SYMMETRIC CONSTITUTIVE MATRIX FOR THE NONLINEAR ANALYSIS OF HYPOELASTIC SOLIDS BASED ON A FORMULATION LEADING TO A NON-SYMMETRIC STIFFNESS MATRIX

H.A. DI RADO; J.L. MROGINSKI; P.A. BENEYTO; A.M. AWRUCH

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING

John Wiley & Sons

Año: 2008 vol. 24 p. 1079 - 1092

1069-8299

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 matriz 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 stresses effects. Important saving in processing time and computer memory may be obtained if a symmetric constitutive matrix is used.