Stabilized finite elements applied to elastoplasticity: I. Mixed displacement–pressure formulation

Commend, S.; Truty, Andrzej; Zimmermann, Thomas

doi:10.1016/j.cma.2004.01.007

Cited by 18 publications

(8 citation statements)

References 8 publications

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“…The material parameters are Young's modulus E = 10 5 and Poisson's ratio m = 0.49999. The solution to this problem is the steady-state solution of the Stokes flow problem in a driven cavity [28].…”

Section: Driven Cavity Flowmentioning

confidence: 99%

Strain smoothing in FEM and XFEM

Bordas

Rabczuk

Nguyen‐Xuan

et al. 2010

Computers & Structures

268

110

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Section: Driven Cavity Flowmentioning

confidence: 99%

Strain smoothing in FEM and XFEM

Bordas

Rabczuk

Nguyen‐Xuan

et al. 2010

Computers & Structures

268

110

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“…For quadrilateral finite elements, this can be overcome by using the Bbar approach 5. Commend et al 30 showed that stabilization is an efficient way of remediating locking for the dry, unsaturated case, for low‐order quadrilateral as well as triangular finite elements. This approach, however, requires a mixed formulation for the geomechanics equations.…”

Section: Numerical Resultsmentioning

confidence: 99%

Stabilization procedures in coupled poromechanics problems: A critical assessment

Preisig

Prévost

2010

Num Anal Meth Geomechanics

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SUMMARYNumerical solutions for problems in coupled poromechanics suffer from spurious pressure oscillations when small time increments are used. This has prompted many researchers to develop methods to overcome these oscillations. In this paper, we present an overview of the methods that in our view are most promising. In particular we investigate several stabilized procedures, namely the fluid pressure Laplacian stabilization (FPL), a stabilization that uses bubble functions to resolve the fine-scale solution within elements, and a method derived by using finite increment calculus (FIC). On a simple one-dimensional test problem, we investigate stability of the three methods and show that the approach using bubble functions does not remove oscillations for all time step sizes. On the other hand, the analysis reveals that FIC stabilizes the pressure for all time step sizes, and it leads to a definition of the stabilization parameter in the case of the FPL-stabilization. Numerical tests in one and two dimensions on 4-noded bilinear and linear triangular elements confirm the effectiveness of both the FPL-and the FIC-stabilizations schemes for linear and nonlinear problems.

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“…, which has been tested by Commend et al . in under the name Laplacian pressure operator scheme. It is also well known that consistently stabilized finite element methods can lead to well‐posed discrete problems for a wide range of displacement/mean‐stress pairs, including equal‐order interpolants on low‐order elements (viz.…”

Section: Governing Equations and Stabilized Mixed Formulationmentioning

confidence: 99%

“…Meanwhile, several authors have continued using standard, unstabilized triangular elements without apparently being bothered by the poor performance that is attributed by many authors to low‐order elements and linear triangles in particular . In a paper on the integration of the Mohr–Coulomb (M–C) yield criterion, Larsson and Runesson use unstructured triangular meshes without any mention of a problem.…”

Section: Introductionmentioning

confidence: 99%

New findings on limit state analysis with unstructured triangular finite elements

Preisig

Prévost

2013

Numerical Meth Engineering

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SUMMARY The emergence of high performance unstructured mesh generators enables the use of low‐order triangles and tetrahedras for a wide variety of problems, where no structured quadrangular mesh can be easily constructed. Some of the results acknowledged by the community of computational mechanics therefore need to be carefully looked at under the light of these recent advances in unstructured and adaptive meshing. In particular, we question evidence of locking during plastic flow, as it has been presented by several authors in the past. We claim that locking can also manifest through stress oscillations. Overshoot of limit loads or displacement locking can be explained by other causes: Insufficient mesh refinement or comparison with analytical solutions that are based on assumptions that are inconsistent with the finite element model. We present a stabilized Galerkin mixed method that allows accurate and converging limit loads to be computed for any elastic‐plastic problem using standard equal‐order interpolation for both displacements and mean stress for low‐order linear triangular elements. The method is attractive for simulations where the cost of meshing is more important than the added computational cost of an additional nodal unknown required by the mixed formulation. Copyright © 2013 John Wiley & Sons, Ltd.

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Stabilized finite elements applied to elastoplasticity: I. Mixed displacement–pressure formulation

Cited by 18 publications

References 8 publications

Strain smoothing in FEM and XFEM

Strain smoothing in FEM and XFEM

Stabilization procedures in coupled poromechanics problems: A critical assessment

New findings on limit state analysis with unstructured triangular finite elements

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