The Earthquake Engineering Online Archive

Penalty formulations for rubber-like elasticity

Simo, Juan C.; Taylor, Robert L.

UCB/SESM-1981/03, Dept. of Civil Engineering, University of California, Berkeley, 1981-11, 30 pages (500/C23/81/03)

The analysis of incompressible rubber-like materials is considered using a penalty function approach. In particular, the necessary compatibility conditions for developing penalty forms for isotropic nonlinear elasticity are addressed, and the commonly used form of strain energy functional leading to a penalty formulation of the incompressibility constraint extended. The Mooney-Rivlin model is used to show how previous developments can lead to physically meaningless situations. For a certain class of incompressible materials, which includes the important Mooney-Rivlin model, a new and particularly simple formulation is proposed. The finite element implementation of this penalty formulation is considered in the appendixes to this report.

Available online: http://nisee.berkeley.edu/documents/SEMM/SEMM-81-03.pdf (1 MB)