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An extension of the penalty function formulation to incompressible hyperelastic solids described by general measure of strain
Author(s) -
Kakavas P. A.,
Chang W. V.
Publication year - 1995
Publication title -
journal of applied polymer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.575
H-Index - 166
eISSN - 1097-4628
pISSN - 0021-8995
DOI - 10.1002/app.1995.070550708
Subject(s) - hyperelastic material , penalty method , constitutive equation , compressibility , finite element method , plane stress , measure (data warehouse) , mathematics , strain energy , function (biology) , mathematical analysis , constraint (computer aided design) , mathematical optimization , computer science , mechanics , physics , geometry , thermodynamics , database , evolutionary biology , biology
The penalty function formulation for incompressible hyperelastic solids was first proposed about 30 years ago. Since then all studies have been limited to invariant type formulation of the strain energy function, although it is well known that this formulation does not correctly describe the behavior of a real material. On the other hand more realistic constitutive equations, based on general measures of the strain only, have been incorporated to mixed finite element algorithms. In this 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 regular Newton–Raphson algorithm. The method is applied to evaluate the stress field in materials subjected to plane strain conditions. Satisfactory agreements have been obtained with analytical solutions when available. © 1995 John Wiley & Sons, Inc.