A COMPRESSIBLE APPROACH IN FINITE-ELEMENT ANALYSIS OF RUBBER-ELASTIC MATERIALS

This paper presents a finite element procedure for rubber-elastic mate rials based on a strain energy function of the compressible type. A br ief review on the material's description and the related numerical met hods is given. A compressible strain energy function is developed by a dding a bulk (dilatational) term to the Ogden-Tschoegl model and is us ed for finite element formulations. An ideal dilatation test is used t o show that the penalty method is equivalent to modifying a strain ene rgy function from an incompressible form to a compressible form and th at the penalty parameter is related to the Lame's constant lambda. The numerical approach to near incompressibility in this work is a natura l penalty method which does not use an artificial penalty function. A method for finite element implementation of a strain energy function i n terms of principal stretches is proposed, in which the stresses and the material moduli are initially calculated in principal directions a nd are then transformed to the axial directions of an active coordinat e system. Two finite element formulations, the total Lagrangian (TL) a nd the updated Lagrangian (UL), are given explicitly. Finite element c odes for plane stress, plane strain, axisymmetric and three-dimensiona l problems are developed. The TL formulation is used in programming ex cept for the three-dimensional code which uses the UL formulation. Num erical experiments are conducted on benchmark problems to show the eff ectiveness of the proposed procedure for the analysis of rubber-elasti c materials. Copyright (C) 1996 Elsevier Science Ltd.