Hyperelastic nature of the Hoek–Brown criterion

Fontana, I.; Bacquaert, G.; Di Pietro, D.A.; Kazymyrenko, K.

doi:10.1016/j.euromechsol.2025.105782

Hyperelastic nature of the Hoek–Brown criterion

Journal Article · Thu Jul 17 00:00:00 EDT 2025 · European Journal of Mechanics. A, Solids

DOI:https://doi.org/10.1016/j.euromechsol.2025.105782· OSTI ID:3025767

Fontana, I. ^[1]; Bacquaert, G. ^[2]; Di Pietro, D.A. ^[3]; Kazymyrenko, K. ^[2]

Univ. of Arizona, Tucson, AZ (United States)
Électricité de France, Palaiseau (France)
Univ. de Montpellier (France)

In this article, we propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or hyperelastic) behavior with plasticity obeying the associated flow rule. Interestingly, we find that a linear yield criterion on the thermodynamical force associated with plasticity results in a quadratic yield criterion in the stress space. This suggests a specific hyperelastic connection between Mohr–Coulomb and Hoek–Brown (or alternatively between Drucker–Prager and Pan–Hudson) yield criteria. We compare the elasto-plastic responses of standard tests for the Drucker–Prager yield criterion using either linear or the suggested hyperbolic elasticity. Notably, the nonlinear case stands out due to dilatancy saturation observed during cyclic loading in the triaxial compression test. We conclude this study with structural finite element simulations that clearly demonstrate the numerical applicability of the proposed model.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Arizona, Tucson, AZ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Computational Science Research & Partnerships (CSRP)

Grant/Contract Number:: SC0024246

OSTI ID:: 3025767

Journal Information:: European Journal of Mechanics. A, Solids, Journal Name: European Journal of Mechanics. A, Solids Vol. 115; ISSN 0997-7538

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (34)

Subdifferential‐based implicit return‐mapping operators in computational plasticity Sysala, Stanislav; Cermak, Martin; Koudelka, Tomáš ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 96, Issue 11 https://doi.org/10.1002/zamm.201500305	journal	June 2016
Conewise linear elastic materials Curnier, Alain; He, Qi-Chang; Zysset, Philippe Journal of Elasticity, Vol. 37, Issue 1 https://doi.org/10.1007/BF00043417	journal	January 1995
A model of nonlinearly hardening materials for complex loading Dafalias, Y. F.; Popov, E. P. Acta Mechanica, Vol. 21, Issue 3 https://doi.org/10.1007/BF01181053	journal	October 1975
The Hoek–Brown Failure Criterion Eberhardt, Erik Rock Mechanics and Rock Engineering, Vol. 45, Issue 6 https://doi.org/10.1007/s00603-012-0276-4	journal	July 2012
Three-Dimensional Failure Criteria Based on the Hoek–Brown Criterion Priest, Stephen Rock Mechanics and Rock Engineering, Vol. 45, Issue 6 https://doi.org/10.1007/s00603-012-0277-3	journal	July 2012
Drucker–Prager Criterion Alejano, Leandro R.; Bobet, Antonio Rock Mechanics and Rock Engineering, Vol. 45, Issue 6 https://doi.org/10.1007/s00603-012-0278-2	journal	July 2012
Mohr–Coulomb Failure Criterion Labuz, Joseph F.; Zang, Arno Rock Mechanics and Rock Engineering, Vol. 45, Issue 6 https://doi.org/10.1007/s00603-012-0281-7	journal	July 2012
Cyclic and Fatigue Behaviour of Rock Materials: Review, Interpretation and Research Perspectives Cerfontaine, B.; Collin, F. Rock Mechanics and Rock Engineering, Vol. 51, Issue 2 https://doi.org/10.1007/s00603-017-1337-5	journal	October 2017
A unified thermoplastic/viscoplastic constitutive model for geomaterials Raude, S.; Laigle, F.; Giot, R. Acta Geotechnica, Vol. 11, Issue 4 https://doi.org/10.1007/s11440-015-0396-6	journal	July 2015
Constitutive relations in plasticity, damage and fracture mechanics based on a work property Marigo, J. J. Nuclear Engineering and Design, Vol. 114, Issue 3 https://doi.org/10.1016/0029-5493(89)90105-2	journal	June 1989
On the validity of the ‘Brazilian’ test for brittle materials Fairhurst, C. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 1, Issue 4 https://doi.org/10.1016/0148-9062(64)90060-9	journal	October 1964
The use of a variable shear modulus in elastic-plastic models for clays Houlsby, G. T. Computers and Geotechnics, Vol. 1, Issue 1 https://doi.org/10.1016/0266-352X(85)90012-6	journal	January 1985
The variational formulation of viscoplastic constitutive updates Ortiz, M.; Stainier, L. Computer Methods in Applied Mechanics and Engineering, Vol. 171, Issue 3-4 https://doi.org/10.1016/S0045-7825(98)00219-9	journal	April 1999
On hyperelasticity for clays Niemunis, Andrzej; Cudny, Marcin Computers and Geotechnics, Vol. 23, Issue 4 https://doi.org/10.1016/S0266-352X(98)00022-6	journal	December 1998
A variational formulation for nonlocal damage models Lorentz, E.; Andrieux, S. International Journal of Plasticity, Vol. 15, Issue 2 https://doi.org/10.1016/S0749-6419(98)00057-6	journal	March 1999
Introducing the open-source mfront code generator: Application to mechanical behaviours and material knowledge management within the PLEIADES fuel element modelling platform Helfer, Thomas; Michel, Bruno; Proix, Jean-Michel Computers & Mathematics with Applications, Vol. 70, Issue 5 https://doi.org/10.1016/j.camwa.2015.06.027	journal	September 2015
Non-linear anisotropic hyperelasticity for granular materials Houlsby, G. T.; Amorosi, A.; Rollo, F. Computers and Geotechnics, Vol. 115 https://doi.org/10.1016/j.compgeo.2019.103167	journal	November 2019
Comportement élastique non linéaire d'un milieu granulaire : approche micromécanique Maalej, Yamen; Dormieux, Luc; Sanahuja, Julien Comptes Rendus. Mécanique, Vol. 335, Issue 8 https://doi.org/10.1016/j.crme.2007.06.002	journal	August 2007
A standard thermodynamic-based extension of the Modified Cam-Clay soil model and its applications Bacquaert, G.; Raude, S.; Alves-Fernandes, V. European Journal of Mechanics - A/Solids, Vol. 103 https://doi.org/10.1016/j.euromechsol.2023.105122	journal	January 2024
Modification of a generalized three-dimensional Hoek–Brown strength criterion Zhang, Qi; Zhu, Hehua; Zhang, Lianyang International Journal of Rock Mechanics and Mining Sciences, Vol. 59 https://doi.org/10.1016/j.ijrmms.2012.12.009	journal	April 2013
The Hoek–Brown failure criterion and GSI – 2018 edition Hoek, E.; Brown, E. T. Journal of Rock Mechanics and Geotechnical Engineering, Vol. 11, Issue 3 https://doi.org/10.1016/j.jrmge.2018.08.001	journal	June 2019
A simplified three-dimensional extension of Hoek-Brown strength criterion Li, Hangzhou; Guo, Tong; Nan, Yalin Journal of Rock Mechanics and Geotechnical Engineering, Vol. 13, Issue 3 https://doi.org/10.1016/j.jrmge.2020.10.004	journal	June 2021
Biaxial behavior of plain concrete of nuclear containment building Lee, Sang-Keun; Song, Young-Chul; Han, Sang-Hoon Nuclear Engineering and Design, Vol. 227, Issue 2 https://doi.org/10.1016/j.nucengdes.2003.09.001	journal	January 2004
The evolution of elastic moduli with increasing crack damage during cyclic stressing of a basalt from Mt. Etna volcano Heap, M. J.; Vinciguerra, S.; Meredith, P. G. Tectonophysics, Vol. 471, Issue 1-2 https://doi.org/10.1016/j.tecto.2008.10.004	journal	June 2009
Elastic Properties of Soils Hicher, Pierre-Yves Journal of Geotechnical Engineering, Vol. 122, Issue 8 https://doi.org/10.1061/(ASCE)0733-9410(1996)122:8(641)	journal	August 1996
Coupling Plasticity and Energy-Conserving Elasticity Models for Clays Borja, Ronaldo I.; Tamagnini, Claudio; Amorosi, Angelo Journal of Geotechnical and Geoenvironmental Engineering, Vol. 123, Issue 10 https://doi.org/10.1061/(ASCE)1090-0241(1997)123:10(948)	journal	October 1997
Empirical Strength Criterion for Rock Masses Hoek, Evert; Brown, Edwin T. Journal of the Geotechnical Engineering Division, Vol. 106, Issue 9 https://doi.org/10.1061/AJGEB6.0001029	journal	September 1980
Behavior of Concrete under Biaxial Stresses Kupfer, Helmut B.; Gerstle, Kurt H. Journal of the Engineering Mechanics Division, Vol. 99, Issue 4 https://doi.org/10.1061/JMCEA3.0001789	journal	August 1973
Soil mechanics and plastic analysis or limit design Drucker, D. C.; Prager, W. Quarterly of Applied Mathematics, Vol. 10, Issue 2 https://doi.org/10.1090/qam/48291	journal	January 1952
Application of thermomechanical principles to the modelling of geotechnical materials Collins, I. F.; Houlsby, G. T. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 453, Issue 1964 https://doi.org/10.1098/rspa.1997.0107	journal	September 1997
Continuum Thermodynamics Germain, P.; Nguyen, Q. S.; Suquet, P. Journal of Applied Mechanics, Vol. 50, Issue 4b https://doi.org/10.1115/1.3167184	journal	December 1983
Gradient Damage Models and Their Use to Approximate Brittle Fracture Pham, Kim; Amor, Hanen; Marigo, Jean-Jacques International Journal of Damage Mechanics, Vol. 20, Issue 4 https://doi.org/10.1177/1056789510386852	journal	November 2010
The Influence of Strains in Soil Mechanics Roscoe, K. H. Géotechnique, Vol. 20, Issue 2 https://doi.org/10.1680/geot.1970.20.2.129	journal	June 1970
A brief history of the development of the Hoek-Brown failure criterion Hoek, Evert; Marinos, Paul Soils and Rocks, Vol. 30, Issue 2 https://doi.org/10.28927/SR.302085	journal	May 2007

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