Uniqueness and localization—I. Associative and non-associative elastoplasticity

Bigoni, Davide; Hueckel, Tomasz

doi:10.1016/0020-7683(91)90205-t

Cited by 214 publications

(109 citation statements)

References 18 publications

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“…However, a comprehensive and rigorous comparison of their theoretical foundations and underlying assumptions is seldom made. Listing all these criteria proves authors suggested the use of loss of strong ellipticity [Bigoni and Hueckel, 1991;Neilsen and Schreyer, 1993], which was shown to coincide with Rice's criterion for associative elasto-plastic models.…”

Section: Introductionmentioning

confidence: 88%

Bifurcation Analysis Versus Maximum Force Criteria in Formability Limit Assessment of Stretched Metal Sheets

Abed‐Meraim

Peerlings

Geers

2014

Int. J. Appl. Mechanics

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The present contribution deals with the prediction of diffuse necking in the context of forming and stretching of metal sheets. For this purpose, two approaches are investigated, namely bifurcation and the maximum force principle, with a systematic comparison of their respective ability to predict necking. While the bifurcation approach is of quite general applicability, some restrictions are shown for the application of maximum force conditions. Although the predictions of the two approaches are identical for particular loading paths and constitutive models, they are generally different, which is even the case for elasticity, confirming the distinct nature of the two concepts. Closed-form expressions of the critical stress and strain states are derived for both criteria in elasto-plasticity and rigid-plasticity for a variety of hardening models. The resulting useful formulas in rigidplasticity are shown to also accurately represent the elasto-plastic critical states for small ratios of the hardening modulus with respect to Young's modulus. Finally, the well-known expression of Swift's diffuse necking criterion, whose foundations are attributed in the literature to the maximum force principle, is shown here to originate from the bifurcation approach instead, providing a sound justification for it.

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Section: Introductionmentioning

confidence: 88%

Bifurcation Analysis Versus Maximum Force Criteria in Formability Limit Assessment of Stretched Metal Sheets

Abed‐Meraim

Peerlings

Geers

2014

Int. J. Appl. Mechanics

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“…Several authors [3,6,16,34,37,42,43,44,48] have analytical and geometrical solutions for the orientation of discontinuity S bands (see Fig. 3) in elasto-plastic materials using different strategies.…”

Section: Orientation Of the Localization Bandmentioning

confidence: 99%

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

et al. 2016

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K: explicit mixed finite elements, stabilization, incompressibility, plasticity, strain softening, strain localization, mesh independence. AbstractThis paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P 1P 1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.

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“…Rudnicki and Rice (1975), and Rice (1976) proposed criterion for formation of shear band and critical orientation of shear band, considering a non-associated ‰ow rule. Based on Rice's work, the general principles of localization of deformation into shear strain band were well established, and they were applied to investigate the thin shear band type localization (Peters et al, 1988;Bardet, 1990;Bigoni and Heueckel, 1991;Szabo, 2000;Lade and Wang, 2001;Heueckel, 2002). The most typical localized deformation observed in geo-materials is linear shear banding.…”

Section: Previous Investigationmentioning

confidence: 99%

Strain Localization in Solid Cylindrical Clay Specimens Using Digital Image Analysis (DIA) Technique

Sachan

Penumadu

2007

Soils and Foundations

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Uniqueness and localization—I. Associative and non-associative elastoplasticity

Cited by 214 publications

References 18 publications

Bifurcation Analysis Versus Maximum Force Criteria in Formability Limit Assessment of Stretched Metal Sheets

Bifurcation Analysis Versus Maximum Force Criteria in Formability Limit Assessment of Stretched Metal Sheets

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

Strain Localization in Solid Cylindrical Clay Specimens Using Digital Image Analysis (DIA) Technique

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