Nonlinear computation of axisymmetric solid rubber deformation (Q1097078)

The paper is of a technical nature and is devoted essentially to the detailed derivation of the element gradient vector and stiffness matrix for the nonlinear finite element analysis of axisymmetric rubber. The technique, which is based on the discrete sampling of the total potential energy of the deformed solid, is a natural extension of the one employed in the nonlinear analysis of rubber membranes [the first author, Int. J. Numer. Methods Eng. 18, 653-660 (1982; Zbl 0482.73064)]. However, in contrast with the thin membrane case exact incompressibility is avoided here and an extra energy term is added for the change of volume work.