Numerical Solution of Problems in Incompressible Finite Elasticity by Augmented Lagrangian Methods - 1. Two-Dimensional and Axisymmetric Problems

A new approach to equilibrium problems in incompressible finite elasticity is discussed. This approach, which is based on the use of a convenient augmented Lagrangian functional, leads to a family of iterative methods which seem very effective for solving this type of elasticity problems once they have been approximated by appropriate finite element methods. The possiblities of the above methods are illustrated by the numerical solution of several problems in two-dimensional and axisymmetric geometries; comparisons with available analytical results are also presented.