A Hypoplastic Model with Isotropic and Oedometric Proportional Paths
Publication: International Journal of Geomechanics
Volume 24, Issue 10
Abstract
To accurately represent the proportional stress–strain behavior observed in granular materials, we extend the hypoplastic model originally proposed by Gudehus and Bauer. This extension incorporates two new tensorial terms. By introducing these terms and their associated coefficients, we establish an implicit relationship for oedometric proportional compression. Our numerical simulations, based on element tests, demonstrate that this extended model effectively describes the isotropic and oedometric proportional stress–strain behavior of granular materials. Furthermore, we outline the process for determining the constitutive parameters and discuss the corresponding calibration methods within this study.
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Acknowledgments
The research for this paper was financially supported by the National Key Research and Development Program of China (2021YFC3001305), the National Natural Science Foundation of China (Grant No. 51809230), and the Qinghai Province Basic Research Program Project (2019-ZJ-7048). We are grateful to the China Scholarship Council (CSC) for the financial support to Dr. Li during his Ph.D. study. Dr. Li wishes to thank Prof. Bauer for his guidance and numerous discussions about hypoplasticity.
References
Bauer, E. 1996. “Calibration of a comprehensive hypoplastic model for granular materials.” Soils Found. 36 (1): 13–26. https://doi.org/10.3208/sandf.36.13.
Bauer, E. 2000. “Conditions for embedding Casagrande’s critical states into hypoplasticity.” Mech. Cohesive-frict. Mater. 5 (2): 125–148. https://doi.org/10.1002/(ISSN)1099-1484.
Bauer, E. 2009. “Hypoplastic modelling of moisture-sensitive weathered rockfill materials.” Acta Geotech. 4 (4): 261–272. https://doi.org/10.1007/s11440-009-0099-y.
Einav, I. 2012. “The unification of hypo-plastic and elasto-plastic theories.” Int. J. Solids Struct. 49 (11–12): 1305–1315. https://doi.org/10.1016/j.ijsolstr.2012.02.003.
Goldscheider, M. 1976. “Grenzbedingung und Fließregel von Sand.” Mech. Res. Commun. 3 (6): 463–468. https://doi.org/10.1016/0093-6413(76)90037-9.
Green, A. E. 1956. “Hypo-Elasticity and Plasticity.” Proc. R. Soc. London, Ser. A 234 (1196): 46–59. https://doi.org/10.1098/rspa.1956.0014.
Gudehus, G. 1996. “A comprehensive constitutive equation for granular materials.” Soils Found. 36 (1): 1–12. https://doi.org/10.3208/sandf.36.1.
Gudehus, G., and D. Mašín. 2009. “Graphical representation of constitutive equations.” Géotechnique 59 (2): 147–151.
Guo, X., C. Peng, W. Wu, and Y. Wang. 2016. “A hypoplastic constitutive model for debris materials.” Acta Geotech. 11 (6): 1217–1229. https://doi.org/10.1007/s11440-016-0494-0.
Herle, I., and G. Gudehus. 1999. “Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies.” Mech. Cohesive-frict. Mater. 4 (5): 461–486. https://doi.org/10.1002/(ISSN)1099-1484.
Huang, W., K. Nübel, and E. Bauer. 2002. “Polar extension of a hypoplastic model for granular materials with shear localization.” Mech. Mater. 34 (9): 563–576. https://doi.org/10.1016/S0167-6636(02)00163-1.
Kast, K. 1992. Mechanisches Verhalten von Granitschüttungen. Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Universität Fridericiana in Karlsruhe, Heft 125 edition.
Kolymbas, D. 1978. Ein nichtlineares viskoplastisches Stoffgesetz für Böden. Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Universität Fridericiana in Karlsruhe, Heft 77 edition.
Kolymbas, D. 1991. “An outline of hypoplasticity.” Arch. Appl. Mech. 61 (3): 143–151. https://doi.org/10.1007/BF00788048.
Li, L. 2018. “Hypoplastic modelling of grain stiffness degradation in granular material.” Ph.D. thesis, Institute of Applied Mechanics, Graz Univ. of Technology.
Li, L., Z. Wang, and E. Bauer. 2016. “Calibration and performance of two different constitutive models for rockfill materials.” Water Sci. Eng. 9 (3): 227–239. https://doi.org/10.1016/j.wse.2016.11.005.
Mašín, D. 2005. “A hypoplastic constitutive model for clays.” Int. J. Numer. Anal. Methods Geomech. 29 (4): 311–336. https://doi.org/10.1002/(ISSN)1096-9853.
Medicus, G. 2014. “Barodesy and its application for clay.” Ph.D. thesis, Dept. of Infrastructure Engineering, Unit of Geotechnical Engineering, Univ. of Innsbruck.
Medicus, G., and W. Fellin. 2017. “An improved version of barodesy for clay.” Acta Geotech. 12 (2): 365–376. https://doi.org/10.1007/s11440-016-0458-4.
Medicus, G., W. Fellin, and D. Kolymbas. 2012. “Barodesy for clay.” Géotech. Lett. 2 (4): 173–180.
Medicus, G., D. Kolymbas, and W. Fellin. 2016. “Proportional stress and strain paths in barodesy.” Int. J. Numer. Anal. Methods Geomech. 40 (4): 509–522. https://doi.org/10.1002/nag.v40.4.
Niemunis, A., and I. Herle. 1997. “Hypoplastic model for cohesionless soils with elastic strain range.” Mech. Cohesive-frict. Mater. 2: 279–299. https://doi.org/10.1002/(ISSN)1099-1484.
von Wolffersdorff, P. 1996. “Hypoplastic relation for granular materials with a predefined limit state surface.” Mech. Cohesive-frict. Mater. 1: 251–271. https://doi.org/10.1002/(ISSN)1099-1484.
Wang, C. 1970. “A new representation theorem for isotropic functions: An answer to Professor G. F. Smith’s criticism of my papers on representations for isotropic functions.” Arch. Ration. Mech. Anal. 36 (3): 166–197. https://doi.org/10.1007/BF00272241.
Wang, S., W. Wu, Z.-Y. Yin, C. Peng, and X. He. 2018. “Modelling the time-dependent behaviour of granularmaterial with hypoplasticity.” Int. J. Numer. Anal. Methods Geomech. 42 (12): 1331–1345. https://doi.org/10.1002/nag.v42.12.
Wu, W., and E. Bauer. 1994. “A simple hypoplastic constitutive model for sand.” Int. J. Numer. Anal. Methods Geomech. 18 (12): 833–862. https://doi.org/10.1002/nag.v18:12.
Wu, W., and D. Kolymbas. 2000. “Hypoplasticity then and now.” In Constitutive modelling of granular materials, edited by D. Kolymbas, 57–105. Berlin, Heidelberg: Springer.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 10 • October 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: May 20, 2023
Accepted: Apr 23, 2024
Published online: Aug 8, 2024
Published in print: Oct 1, 2024
Discussion open until: Jan 8, 2025
ASCE Technical Topics:
- Compression
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering materials (by type)
- Engineering mechanics
- Granular materials
- Isotropy
- Material mechanics
- Material properties
- Materials engineering
- Model accuracy
- Models (by type)
- Numerical models
- Simulation models
- Solid mechanics
- Structural dynamics
- Structural engineering
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