2009
DOI: 10.1002/nme.2734
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An adaptive stabilization strategy for enhanced strain methods in non‐linear elasticity

Abstract: 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… Show more

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Cited by 14 publications
(4 citation statements)
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“…All of the options listed above can furthermore be used with an elementwise average Jacobian in analogy to (36) given by…”
Section: Enhanced Deformation Gradientmentioning
confidence: 99%
See 1 more Smart Citation
“…All of the options listed above can furthermore be used with an elementwise average Jacobian in analogy to (36) given by…”
Section: Enhanced Deformation Gradientmentioning
confidence: 99%
“…Thus, there is a plethora of publications on the method in various fields such as shell structures, modeling of failure, and even diffusion problems (see, eg, works). In this work, however, focus is put on 2D and 3D nonlinear solid mechanics (see, eg, works among others).…”
Section: Introductionmentioning
confidence: 99%
“…The appearance of an hourglass mode in the context of nonlinear enhanced strain methods has first been observed by de Souza Neto et al , and Wriggers and Reese after the method had been extended to geometrically nonlinear problems by Simo and coworkers . Once the problem was detected, numerous methods have been proposed to overcome the instability . However, most of the methods are either difficult to implement or parameter‐dependent and often stable in one case but unstable in another.…”
Section: Introductionmentioning
confidence: 99%
“…Consequently, it is possible to interpret the role of the DG-derivative of a discontinuous displacement field as transforming displacement jumps into 'enhanced' strain fields. In fact, the role of the lifting operator shares many traits with that of strain enhancements in the contexts of enhanced-strain methods, see [34].…”
Section: Dg Methods For the Enrichment Boundarymentioning
confidence: 98%