Numerical Solution of Problems in Incompressible Finite Elasticity by Augmented Lagrangian Methods II. Three-Dimensional Problems

In a first paper [SIAM J. Appl. Math., 42 (1982), pp. 400–429] we introduced an augmented Lagrangian methodology for solving equilibrium problems in incompressible finite elasticity, and then applied it to the solution of several two-dimensional and axisymmetric test problems. In this second paper we extend our methods to the solution of genuine three-dimensional problems; actually using these augmented Lagrangian techniques we can reduce the solution of these complicated nonlinear, nonconvex problems, to the solution of a sequence of linear problems and also to the solution of a sequence of minimization problems for convex functionals on convex sets. The capabilities of our methods are illustrated by the results of numerical experiments.