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Augmented Lagrangian approach to deriving discontinuous Galerkin methods for nonlinear elasticity problems
Author(s) -
Hansbo Peter,
Larson Mats G.
Publication year - 2022
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.7039
Subject(s) - hyperelastic material , tangent stiffness matrix , discretization , mathematics , tangent , elasticity (physics) , galerkin method , augmented lagrangian method , mathematical analysis , nonlinear system , finite element method , stiffness , discontinuous galerkin method , nonlinear elasticity , stiffness matrix , mathematical optimization , geometry , physics , quantum mechanics , thermodynamics
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.