Algorithmic issues for three-invariant hyperplastic Critical State models

Coombs, William M.; Crouch, Roger S.

doi:10.1016/j.cma.2011.03.019

Cited by 18 publications

(21 citation statements)

References 37 publications

(56 reference statements)

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“…The Newton process continues until the L 2 norm of the residuals converge to a given tolerance. A common problem in implicit stress integration is the stability of the algorithm due to the form of the yield function outside of the yield envelope [5]. Unless care is taken when specifying the yield equation it is possible to obtain a form that contains local minima, or even ancillary f = 0 loci in the inadmissible region of stress space.…”

Section: Stress Integration Algorithmmentioning

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: Stress Integration Algorithmmentioning

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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“…α and γ determine the shape of the surface (as shown by Coombs and Crouch (2011) for the case when β ij = 0). If R = 1 then p χ = γp c /2 and s χ ij = γp c β ij /2; that is, the inner and outer surfaces coincide.…”

Section: Rate Of Dissipationmentioning

confidence: 99%

“…The liquid limit is the moisture content at which a standard V-groove cut into the soil just closes when shaken using standard equipment. (iii) an anisotropic bubble model 17 (similar to those models introduced by Mróz and Norris (1979) and Wood (2000, 2001), albeit with a different energy-conserving elasticity law), (iv) SANIclay (Dafalias et al, 2006) and (v) the isotropic two-parameter hyperplastic model (Coombs and Crouch, 2011). For all of the simulations, the constitutive models started from a …”

Section: Model Comparisons With Experimentsmentioning

confidence: 99%

“…Such single-surface models fail to capture the progressive plastic strains which can occur within the conventional yield surface 3 .Φ 2 in (2) is introduced to account for this dissipation. Following the procedure outlined by Collins (2003), and later used by Coombs and Crouch (2011), the inner surface is obtained as…”

Section: Rate Of Dissipationmentioning

confidence: 99%

“…Here, following Coombs and Crouch (2011), the rate of the evolution of the size of the outer surface is defined aṡ…”

Section: Isotropic Hardening/softeningmentioning

confidence: 99%

See 2 more Smart Citations

A unique Critical State two-surface hyperplasticity model for fine-grained particulate media

Coombs¹,

Crouch²,

Augarde³

2013

Journal of the Mechanics and Physics of Solids

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NOTICE: this is the author's version of a work that was accepted for publication in Journal of the Mechanics and Physics of Solids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Journal of the Mechanics and Physics of Solids, 61, 1, 2013, 10.1016/j.jmps.2012.08.002. Additional information: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.

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Continuously unique anisotropic critical state hyperplasticity

Coombs

2016

Int. J. Numer. Anal. Meth. Geomech.

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Summary This paper presents the theoretical development and methodological motivation of a single surface anisotropic hyperplasticity model. The model extends the isotropic family of models developed by Coombs and Crouch by: (i) introducing anisotropic shearing into the yield surface, (ii) relating two of the material constants to a single physical quantity and (iii) using a more physically realistic pressure sensitive elastic free energy function. This model overcomes the difficulty of determining the constants of the isotropic two‐parameter surface by analytically relating them to a single experimentally measurable physical quantity, namely the normalised hydrostatic position of the Critical State. This provides a model with a Critical State surface that is constant throughout the loading process, invariant of the level of anisotropy inherent in the yield envelope. The model is compared with experimental data from triaxial tests on Lower Cromer Till, contrasted against the SANIclay model and the recent model of Yang et al. (2015) as well as being compared with rarely considered experimental data from hollow cylinder tests on London Clay. Copyright © 2016 John Wiley & Sons, Ltd.

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Algorithmic issues for three-invariant hyperplastic Critical State models

Cited by 18 publications

References 37 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

A unique Critical State two-surface hyperplasticity model for fine-grained particulate media

Continuously unique anisotropic critical state hyperplasticity

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