An exact implementation of the Hoek–Brown criterion for elasto-plastic finite element calculations

Clausen, Johan; Damkilde, Lars

doi:10.1016/j.ijrmms.2007.10.004

Cited by 51 publications

(34 citation statements)

References 21 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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“…The first procedure of the algorithm is the calculation of the elastic trial stresses in general stress space and the transformation of the trial stresses from general stress space to principal stress space . From the first procedure, the three principal trial stresses are calculated and arranged as

σ_{1}^{trial} \geq σ_{2}^{trial} \geq σ_{3}^{trial}

, then the yield condition is checked with the following equations:

F^{trial} = σ_{1}^{trial} - \frac{a}{1 + b} ((), b σ_{2}^{trial} + σ_{3}^{trial}) - σ_{t}^{0} \leq 0, when σ_{2}^{trial} \leq \frac{σ_{1}^{trial} + α σ_{3}^{trial}}{1 + α}

F^{' trial} = \frac{1}{1 + b} ((), σ_{1}^{trial} + b σ_{2}^{trial}) - a σ_{3}^{trial} - σ_{t}^{0} \leq 0, when σ_{2}^{trial} \geq \frac{σ_{1}^{trial} + α σ_{3}^{trial}}{1 + α}

where

σ_{t}^{0}

is the initial tensile yield strength at the current step.…”

Section: The Framework Of Return Mapping Algorithm For Unified Strengmentioning

confidence: 99%

“…Substituting σ 1 = σ 2 = σ 3 into Equation or , the yield function at the apex can be rewritten as

(1 - α) σ_{m} = σ_{t}, when σ_{1} = σ_{2} = σ_{3}

where σ m =( σ 1 + σ 2 + σ 3 )/3. At the apex (Figure ), the general constitutive equation for return mapping is given by Perić and Neto as follows:

σ_{m} = σ_{m}^{trial} - K normalΔ ϵ_{normalV}^{p}

where

normalΔ ϵ_{normalV}^{p}

is the volumetric plastic strain increment. For UST model,

normalΔ ϵ_{normalV}^{p}

is written as

normalΔ ϵ_{normalV}^{p} = (1 - a) normalΔ {\overset{ϵ}{false}}^{p}

where

normalΔ {\overset{ϵ}{false}}^{p}

is the equivalent plastic strain increment.…”

Section: The Framework Of Return Mapping Algorithm For Unified Strengmentioning

confidence: 99%

“…The first procedure of the algorithm is the calculation of the elastic trial stresses in general stress space and the transformation of the trial stresses from general stress space to principal stress space [16]. From the first procedure, the three principal trial stresses are calculated and arranged as trial…”

Section: The Framework Of Return Mapping Algorithm For Unified Strengmentioning

confidence: 99%

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A return mapping algorithm for unified strength theory model

Chen

2015

Numerical Meth Engineering

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Summary A return mapping algorithm in principal stress space for unified strength theory (UST) model is presented in this paper. In contrast to Mohr–Coulomb and Tresca models, UST model contains two planes and three corners in the sextant of principal stress space, and the apex is formed by the intersection of 12 corners rather than the six corners of Mohr–Coulomb in the whole principal stress space. In order to utilize UST model, the existing return mapping algorithm in principal stress space is modified. The return mapping schemes for one plane, middle corner, and apex of UST model are derived, and corresponding consistent constitutive matrices in principal stress space are constructed. Because of the flexibility of UST, the present model is not only suitable for analysis based on the traditional yield functions, such as Mohr–Coulomb, Tresca, and Mises, but might also be used for analysis based on a series of new failure criteria. The accuracy of the present model is assessed by the iso‐error maps. Three numerical examples are also given to demonstrate the capability of the present algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

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“…The main aim of the calculations is to determine the failure loads, which is independent of the chosen values of E and ν. For the plastic stress update, a method analogous to the one for a HoekBrown material is employed, see Clausen and Damkilde [22]. The footing is assumed to be rigid and perfectly rough.…”

Section: Finite Element Calculationsmentioning

confidence: 99%

The Bearing Capacity of Circular Footings in Sand: Comparison between Model Tests and Numerical Simulations Based on a Nonlinear Mohr Failure Envelope

Krabbenhøft

Clausen

Damkilde

2012

Advances in Civil Engineering

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This paper presents the results of a series of triaxial tests with dry sand at confining pressures varying from 1.5 kPa to 100 kPa at relative densities of 0.20, 0.59, and 0.84. The results, which are in reasonable accordance with an equation given by Bolton, show that the friction angle is strongly dependent on the stress level and on the basis of the test results, a nonlinear Mohr failure criterion has been proposed. This yield criterion has been implemented in a finite element program and an analysis of the bearing capacity of a circular shaped model foundation, diameter 100 mm, has been conducted. Comparisons have been made with results from 1g model scale tests with a foundation of similar size and a good agreement between numerical results and test results has been found.

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An exact implementation of the Hoek–Brown criterion for elasto-plastic finite element calculations

Cited by 51 publications

References 21 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 return mapping algorithm for unified strength theory model

The Bearing Capacity of Circular Footings in Sand: Comparison between Model Tests and Numerical Simulations Based on a Nonlinear Mohr Failure Envelope

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