Consistent Linearization for the Exact Stress Update of Prandtl-Reuss Non-Hardening Elastoplastic Models

Zhai, Wei; Perić, D.; Owen, D. R. J.

doi:10.1002/(sici)1097-0207(19960415)39:7<1219::aid-nme901>3.0.co;2-7

Cited by 26 publications

(10 citation statements)

References 15 publications

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“…In the case of von Mises plasticity the NURBS approach was compared with an exact implementation [19,38] demonstrating that the errors in the process are the same as that on a convectional bE method and that for a boundary value simulation the model has excellent agreement with the exact implementation. Asymptotic quadratic convergence of the global out-of-balance force has also been demonstrated validating the algorithmic consistent tangent.…”

Section: Discussionmentioning

confidence: 98%

“…The problem was analysed using both the NURBS implementation of the von Mises yield surface and the exact implementation of Prandtl-Reuss plasticity of Wei et al [38] 3 . The load versus displacement response of the two models is nearly identical (as shown in Figure 8) and both the models converge to the analytical solution with mesh refinement.…”

Section: Notched Platementioning

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: Discussionmentioning

confidence: 98%

Section: Notched Platementioning

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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“…The problem was initially presented by Nagtegaal et al [11] for small strain plasticity to demonstrate the spurious response of standard finite-elements and was subsequently re-analysed in a number of papers [20,21,19]. The plate had a Young's modulus of 206.9GPa, Poisson's ratio of 0.29 and was modelled using an exact implementation of the elastic-perfectly plastic Prandtl-Reuss constitutive model [23]. The yield function for the associated flow model can be expressed as…”

Section: Elasto-plastic Double-notched Platementioning

confidence: 99%

Rotationally invariant distortion resistant finite-elements

Cowan

Coombs

2014

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-prot 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. AbstractThe predictive capability of conventional iso-parametric finite-elements deteriorates with mesh distortion. In the case of geometrically non-linear analysis, changes in geometry causing severe distortion can result in negative Jacobian mapping between the local and global systems resulting in numerical breakdown. This paper presents a finite-element formulation that is resistant to irregular mesh geometries and large element distortions whilst remaining invariant to rigid body motion. The predictive capabilites of the family of finiteelements are demonstrated using a series of geometrically non-linear analyses including an elastic cantilever beam and an elasto-plastic double notched specimen.

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“…Krieg and Krieg [2] showed an analytical solution for perfectly plastic von Mises model by using the constant strain rate assumption. Wei [3] derived the stress update formula with the consistent linearization. Szabó [4], who developed the partial analytical solution proposed by Ristinmaa and Tryding [5], achieved a semi-analytical solution for the purely linear isotropic hardening von Mises elastoplastic model.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric analysis of linear isotropic and kinematic hardening elastoplasticity

Nguyen

Cong

et al. 2017

Vietnam J. Mech.

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Abstract. Material nonlinearity is of great importance in many engineering problems. In this paper, we exploit NURBS-based isogeometric approach in solving materially nonlinear problems, i.e. elastoplastic problems. The von Mises model with linear isotropic hardening and kinematic hardening is presented, and furthermore the method can also be applied to other elastoplastic models without any loss of generality. The NURBS basis functions allow us to describe exactly the curved geometry of underlying problems and control efficiently the accuracy of approximation solution. Once the discretized system of non-linear equilibrium equation is obtained, the Newton-Raphson iterative scheme is used. Several numerical examples are tested. The accuracy and reliability of the proposed method are verified by comparing with results from ANSYS Workbench software.

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Consistent Linearization for the Exact Stress Update of Prandtl-Reuss Non-Hardening Elastoplastic Models

Cited by 26 publications

References 15 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

Rotationally invariant distortion resistant finite-elements

Isogeometric analysis of linear isotropic and kinematic hardening elastoplasticity

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