AN EXTENSION OF THE PENALTY-FUNCTION FORMULATION TO INCOMPRESSIBLE HYPERELASTIC SOLIDS DESCRIBED BY GENERAL MEASURE OF STRAIN

The penalty function formulation for incompressible hyperelastic solid s was first proposed about 30 years ago. Since then all studies have b een limited to invariant type formulation of the strain energy functio n, although it is well known that this formulation does not correctly describe the behavior of a real material. On the other hand more reali stic constitutive equations, based on general measures of the strain o nly, have been incorporated to mixed finite element algorithms. In thi s article, a penalty function formulation is proposed for the analysis of stress field in materials with constitutive equations based on the general measure of strain. The reduced integration method is used to weaken the penalty constraint in order to obtain meaningful numerical results. The incremental equilibrium equations are solved using the re gular Newton-Raphson algorithm. The method is applied to evaluate the stress field in materials subjected to plane strain conditions. Satisf actory agreements have been obtained with analytical solutions when av ailable. (C) 1995 John Wiley and Sons, Inc.