Premium
An adaptive stabilization strategy for enhanced strain methods in non‐linear elasticity
Author(s) -
Ten Eyck Alex,
Lew Adrian
Publication year - 2009
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.2734
Subject(s) - linear elasticity , elasticity (physics) , mathematical optimization , heuristics , quasistatic process , mathematics , range (aeronautics) , compressibility , discontinuous galerkin method , computer science , finite element method , engineering , mechanics , physics , structural engineering , quantum mechanics , thermodynamics , aerospace engineering
This paper proposes and analyzes an adaptive stabilization strategy for enhanced strain (ES) methods applied to quasistatic non‐linear elasticity problems. The approach is formulated for any type of enhancements or material models, and it is distinguished by the fact that the stabilization term is solution dependent. The stabilization strategy is first constructed for general linearized elasticity problems, and then extended to the non‐linear elastic regime via an incremental variational principle. A heuristic choice of the stabilization parameters is proposed, which in the numerical examples proved to provide stable approximations for a large range of deformations, different problems and material models. We also provide explicit lower bounds for the stabilization parameters that guarantee that the method will be stable. These are not advocated, since they are generally larger than the ones based on heuristics, and hence prone to deteriorate the locking‐free behavior of ES methods. Numerical examples with two different non‐linear elastic models in thin geometries and incompressible situations show that the method remains stable and locking free over a large range of deformations. Finally, the method is strongly based on earlier developments for discontinuous Galerkin methods, and hence throughout the paper we offer a perspective about the similarities between the two. Copyright © 2009 John Wiley & Sons, Ltd.