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

The authors previously 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. They now extend their methods to the solution of genuine three-dimensional problems; using these augmented Lagrangian techniques they 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 the methods are illustrated by the results of numerical experiments.