C.H. Liu, G. Hofstetter, H.A. Mang:
"Efficient 3D Finite Element Analysis of Rubber-Like Materials";
ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 73 (1993), 7/8; T906 - T907.
Rubber-like materials are characterized by a high ratio of bulk to shearing stiffness, resulting in a nearly incompressible bahvior. Thus, within the framework of the finite element method a pure displacement formulation leads to numerical problems, well knwon as the locking phenomenon. Several numerical tecniques have been proposed within the last two decades to overcome this drawback. Popular formulations for (nearly) incompressible behavior are a displacement method with reduced or selective integration [2], penalty-type formulations [3] and mixed methods [1, 4, 7] including the Langrage multiplier method. However, many of these papers are restricted to linear-elastic analyses and /or to two-dimensional problems. Up to now only relatively few papers on 3D FE-analyses of (nearly) incompressible rubber-like materials at finite strains have been published. Moreover, some of them semm to suffer from deficiences.[1] Scharnhorst, T.; Pian, T.H.H.: Finite element analysis of rubber-like materials by a mixed model. Internat. J. Numer. MEth. Eng. 12 (1978), 665-676.
[2] Malkus, D.S.; Hughes, T.J.R.: Mixed finite element methods - reduced and selective integration techniques: a unification of concepts. Computat. Meth. Apll. Mech. Eng. 15 (1978), 63-81.
[3] Simo, J.C.; Tylor, R.L.: Penalty function formulations for incompressible nonlinear elastoplastics. Computat. Meth. Appl. Mech. Eng. 35 (1982), 107-118.
[4] Sussman, T.; Bathe, K.J.: A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Comput. sTruct. 26 (1987) 1/2, 357-409.
[7] Simo, J.C.; Taylor, R.L.: Quasi-imcompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Computat. Meth. Appl. Mech. Eng. 85 (1991), 273-310.