Elasto‐plastic stress analysis. A generalization for various contitutive relations including strain softening

Nayak, Gopinatha; Zienkiewicz, O. C.

doi:10.1002/nme.1620050111

Cited by 464 publications

(108 citation statements)

References 21 publications

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“…It is merely noted that several approaches are possible. One of the classical approaches is due to Nayak and Zienkiewicz (1972) and consists in using only one yield function in combination with a rounding offprocedure for points at which two planes of the yield function meet (so-called corner points). The authors use a different procedure in which equation (4.24) is incorporated exactly.…”

Section: Extension To Three-dimensional Stress Statesmentioning

confidence: 99%

Non-Associated Plasticity for Soils, Concrete and Rock

Vermeer

Borst²

1998

Physics of Dry Granular Media

341

357

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Section: Extension To Three-dimensional Stress Statesmentioning

confidence: 99%

Non-Associated Plasticity for Soils, Concrete and Rock

Vermeer

Borst²

1998

Physics of Dry Granular Media

341

357

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“…The plasticity relations available are those based on the use of the yon Mises yield condition and the Drucker-Prager yield condition. Both forms of describing material behavior have been employed extensively in practice [2,[18][19][20], Using the von Mises criterion, linear isotropic hardening can be assumed. In analysis using the Drucker-Prager yield condition, the material is assumed to be elasticperfectly plastic.…”

Section: 3 Elastic-plastic Materials Modelsmentioning

confidence: 99%

“…The endeavor to perform nonlinear analyses has steadily increased in recent years [1][2][3][4]. The safety of a structure may be increased and the cost reduced if a nonlinear analysis can be carried out.…”

Section: Introductionmentioning

confidence: 99%

NONSAP — A nonlinear structural analysis program

Bathe

Wilson

1974

Nuclear Engineering and Design

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The current version of the computer program NONSAP for linear and nonlinear, static and dynamic finite element analysis is presented. The solution capabilities, the numerical techniques used, the finite element library, the logical construction of the program and storage allocations are discussed. The solutions of some sample problems considered during the development of the program are presented.

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“…Explicit methods stem from the work of Ilyushin's [13] method of successive elastic solutions and was subsequently applied to the Prandtl-Reuss constitutive model (von Mises yield surface with linear isotropic elasticity) by Mendelson [21]. Nayak and Zienkiewicz [24] were the first to formulate a general explicit stress integration procedure for use within the finite element method and several models have been subsequently implemented using their method. However, the major drawback of these methods is that they do not enforce the consistency condition at the end of the stress-strain path [37].…”

Section: Introductionmentioning

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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Elasto‐plastic stress analysis. A generalization for various contitutive relations including strain softening

Cited by 464 publications

References 21 publications

Non-Associated Plasticity for Soils, Concrete and Rock

Non-Associated Plasticity for Soils, Concrete and Rock

NONSAP — A nonlinear structural analysis program

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

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