The aim of this paper is first to describe a decomposition principle by augmented Lagrangians which can be used to simplify the solution of some variational problems having a special structure. Associated with this decomposition principle are some iterative methods which appear to be related, in some particular cases, to alternating direction iterative methods. The above principle and methods are then applied to the solution of two particular problems in finite elasticity:

the calculation of large displacements for a class of flexible, inextensible pipe lines

the mechanical behavior of incompressible two-dimensional Mooney-Rivlin materials