An efficient return algorithm for non-associated plasticity with linear yield criteria in principal stress space

Clausen, Johan; Damkilde, Lars; Andersen, Lars Vabbersgaard

doi:10.1016/j.compstruc.2007.04.002

Cited by 81 publications

(48 citation statements)

References 12 publications

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“…The normalised pressure versus displacement response is shown in Figure 9 for both the NURBS yield surface (black-dashed line) and for a conventional backward Euler implementation of the model (thick grey line) based on the work of Clausen et al [4]. The results are indistinguishable with both simulations having an error of 0.8% compared to the analytical limit of 2p/σ y = 2 + π, where p is the average pressure under the footing.…”

Section: Rigid Footingsupporting

confidence: 68%

“…The normalised error measure (31) is used but the exact return stress is determined from a conventional bE implementation of the model based on the work of Clausen et al [4]. Due to the planar nature of the Tresca yield surface, the updated stress from the bE algorithm will be exact provided that the stress increment should not cause the return stress state to cross between sextants of stress space.…”

Section: Tresca Corner Roundingmentioning

confidence: 99%

“…This section provides that tangent following the approach of Clausen et al [2][3][4]. The tangent is first constructed in principal stress space and then transformed into six-component stress space using the eigenvectors associated with the trial elastic strain state (see Appendix B for details).…”

Section: Algorithmic Consistent Tangentmentioning

confidence: 99%

“…where [D e G ] is a three-by-three matrix containing the shear components of the elastic stiffness matrix, the modification matrix for the shear components is given by [4] […”

Section: Six-component Stress Spacementioning

confidence: 99%

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NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

Coombs

Petit²,

Motlagh

2016

Computer Methods in Applied Mechanics and Engineering

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. (2016) 'NURBS plasticity : yield surface representation and implicit stress integration for isotropic inelasticity.', Computer methods in applied mechanics and engineering., 304 . pp. 342-358. Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn numerical analysis the failure of engineering materials is controlled through specifying yield envelopes (or surfaces) that bound the allowable stress in the material. However, each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case. These equations impact on the numerical implementation, specifically relating to stress integration, of the models and therefore a separate algorithm must be constructed for each model. This paper presents, for the first time, a way to construct yield surfaces using techniques from non-uniform rational basis spline (NURBS) surfaces, such that any isotropic convex yield envelope can be represented within the same framework. These surfaces are combined with an implicit backward-Euler-type stress integration algorithm to provide a flexible numerical framework for computational plasticity. The algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration. The performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models.

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Section: Rigid Footingsupporting

confidence: 68%

Section: Tresca Corner Roundingmentioning

confidence: 99%

Section: Algorithmic Consistent Tangentmentioning

confidence: 99%

“…where [D e G ] is a three-by-three matrix containing the shear components of the elastic stiffness matrix, the modification matrix for the shear components is given by [4] […”

Section: Six-component Stress Spacementioning

confidence: 99%

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NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

Coombs

Petit²,

Motlagh

2016

Computer Methods in Applied Mechanics and Engineering

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“…First the constitutive model according to simple Mohr-Coulomb criterion is modeled. Here the return mapping algorithm introduced by Clausen et al, [23] is coded in UMAT and inserted as UGM constitutive model. In the second simulation effect of shakedown as stated in (5) is studied.…”

Section: Modeling Of Layered Flexible Pavementmentioning

confidence: 99%

Simulation of Shakedown Behavior in Pavement’s Granular Layer

Ghadimi¹,

Nega²,

Nikraz³

2015

IJET

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Abstract-While in the design of flexible pavement the significance of asphalt layers is understood, the role of granular layers supporting the asphalt layers should not be underestimated. The behavior of granular layers used in base, sub-base or subgrade layer of flexible pavement is complicated due to nonlinear elastoplastic response of materials subjected to dynamic load of traffic. Shakedown theory integrated with Mohr-Coulomb criterion is applied to simulate the response of granular layers to dynamic loading in a numerical analysis. The results of analysis is then compared to simple the results of modeling without considering shakedown effects and the conclusion is drawn.

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Evaluation of material point method for use in geotechnics

Sołowski

Sloan

2014

Num Anal Meth Geomechanics

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SUMMARYThe first part of the paper presents a material point method solution for the bearing capacity of a deep foundation in purely cohesive soil, which is a widely known engineering problem. The results computed with the generalised interpolation material point method are compared to the results obtained previously with an advanced limit analysis code. The second part of the paper shows material point method simulations of collapsing piles of granular material and compares the results with experimental observations from the literature. The problems considered are problematic to solve using the displacement finite element method as they generally include very large deformations.

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An efficient return algorithm for non-associated plasticity with linear yield criteria in principal stress space

Cited by 81 publications

References 12 publications

NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

Simulation of Shakedown Behavior in Pavement’s Granular Layer

Evaluation of material point method for use in geotechnics

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