Augmented Lagrangian approach to deriving discontinuous Galerkin methods for nonlinear elasticity problems

We use the augmented Lagrangian formalism to derive discontinuous Galerkin (DG) formulations for problems in nonlinear elasticity. In elasticity, stress is typically a symmetric function of strain, leading to symmetric tangent stiffness matrices in Newton's method when conforming finite elements are used for discretization. By use of the augmented Lagrangian framework, we can also obtain symmetric tangent stiffness matrices in DG methods. We suggest two different approaches and give examples from plasticity and from large deformation hyperelasticity.

Automated summary

This article introduces the use of augmented Lagrangian formalism to derive discontinuous Galerkin methods for problems in nonlinear elasticity, and provides examples from plasticity and large deformation hyperelasticity.