Efficient return algorithms for associated plasticity with multiple yield planes

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

doi:10.1002/nme.1595

Cited by 70 publications

(69 citation statements)

References 19 publications

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“…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%

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: Algorithmic Consistent Tangentmentioning

confidence: 99%

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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“…As Clausen et al [4] have shown, the elasto-plastic consistent tangent for a hydrostatic apex return is simply given by…”

Section: Stress Origin Consistent Tangentmentioning

confidence: 99%

“…The consistent tangent for a corner return is obtained following the approach given by Clausen et al [4]. By considering the vector orientation of the edge…”

Section: Compression Meridian Consistent Tangentmentioning

confidence: 99%

“…where [I] is the sixth-order identity matrix [4]. In principal stress space [Q] can be calculated as…”

Section: Compression Meridian Consistent Tangentmentioning

confidence: 99%

“…Section 3 describes the stress return strategies for the three regions where the elastic trial stress may lie. The approach, when returning to the compression meridian or tensile apex, follows Clausen et al's method [4]. When returning elsewhere, finding the closest point to the surface in energy-mapped space [5] requires the solution of a quartic.…”

Section: Introductionmentioning

confidence: 99%

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Reuleaux plasticity: Analytical backward Euler stress integration and consistent tangent

Coombs

Crouch

Augarde

2010

Computer Methods in Applied Mechanics and Engineering

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The 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. AbstractAnalytical backward Euler stress integration is presented for a deviatoric yielding criterion based on a modified Reuleaux triangle. The criterion is applied to a cone model which allows control over the shape of the deviatoric section, independent of the internal friction angle on the compression meridian. The return strategy and consistent tangent are fully defined for all three regions of principal stress space in which elastic trial states may lie. Errors associated with the integration scheme are reported. These are shown to be less than 3% for the case examined. Run time analysis reveals a 2.5-5.0 times speed-up (at a material point) over the iterative Newton-Raphson backward Euler stress return scheme. Two finite-element analyses are presented demonstrating the speed benefits of adopting this new formulation in larger boundary value problems. The simple modified Reuleaux surface provides an advance over Mohr-Coulomb and Drucker-Prager yield envelopes in that it incorporates dependencies on both the Lode angle and intermediate principal stress, without incurring the run-time penalties of more sophisticated models.

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Algorithms for a strain‐based plasticity criterion for bone

Pankaj

Donaldson

2012

Numer Methods Biomed Eng

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A range of stress-based plasticity criteria have been employed in the finite element analysis of the post-elastic behaviour of bone. There is some recognition now that strain-based criteria are more suitable for this material because they better represent its behaviour. Moreover, because bone yields at relatively isotropic strains, a strain-based criterion requires fewer material parameters unlike those required for a stress-based criterion. Based on a minimum and maximum principal strain criterion, a robust strain-based plasticity algorithm is developed. As the criterion comprises six piecewise linear surfaces in principal strain space, it has a number of singular regions. Singularity indicators are developed to direct the algorithm to make appropriate plastic corrector returns when singularity regions are encountered. The developed algorithms permit a plastic corrector to be achieved in a single iterative step in all cases. A range of benchmark tests are developed and conducted after implementing the algorithm in a finite element package. These tests show that the constitutive behaviour is as expected.

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Efficient return algorithms for associated plasticity with multiple yield planes

Cited by 70 publications

References 19 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

Reuleaux plasticity: Analytical backward Euler stress integration and consistent tangent

Algorithms for a strain‐based plasticity criterion for bone

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