AUGMENTED LAGRANGIANS IN FINITE ELASTICITY AND IN PLASTICITY.

Two kinds of nonlinearity are involved in penetration mechanics: yielding and large deformations. Each of them separately can be numerically treated by the augmented Lagrangian techniques described. As a first step toward their eventual use in case where both nonlinearities are present, this paper describes augmented Lagrangian methods in a rather abstract form, which covers a large spectrum of applications. The general frame in which augmented Lagrangians are applied to nonlinear solid mechanics is presented. These techniques are illustrated by the numerical solution of equilibrium problems in incompressible finite elasticity. A second example is given, concerning limit load computation in plasticity.