Plastic-Energy Dissipation in Pressure-Dependent Materials
Publication: Journal of Engineering Mechanics
Volume 146, Issue 3
Abstract
A thermodynamics-based energy analysis approach for pressure-dependent materials is presented. Formulation of plastic free energy and plastic dissipation for the nonassociated Drucker-Prager plasticity model is derived based on thermodynamics. It is proven that the proposed energy computation formulation always gives nonnegative incremental plastic dissipation, as required by the second law of thermodynamics. The presented methodology is illustrated using numerical simulations of Toyoura sand and Sacramento River sand under different loading conditions. Multidirectional loading and pressure dependency effects on plastic dissipation are investigated. The continuous, nonnegative dissipation of mechanical energy in pressure-dependent frictional materials under complex three-dimensional cyclic loading was properly modeled.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported in part by the US Department of Energy.
References
Armstrong, P., and C. Frederick. 1966. A mathematical representation of the multiaxial Bauschinger effect. Central Electricity Generating Board.
Bardet, J. P., and W. Choucair. 1991. “A linearized integration technique for incremental constitutive equations.” Int. J. Numer. Anal. Methods Geomech. 15 (1): 1–19. https://doi.org/10.1002/nag.1610150102.
Ching, J., G.-H. Lin, J.-R. Chen, and K.-K. Phoon. 2017. “Transformation models for effective friction angle and relative density calibrated based on generic database of coarse-grained soils.” Can. Geotech. J. 54 (4): 481–501. https://doi.org/10.1139/cgj-2016-0318.
Collins, I. F. 2002. “Associated and non-associated aspects of the constitutive laws for coupled elastic/plastic materials.” Int. J. Geomech. 2 (2): 259–267. https://doi.org/10.1061/(ASCE)1532-3641(2002)2:2(259).
Collins, I. F. 2003. “A systematic procedure for constructing critical state models in three dimensions.” Int. J. Solids Struct. 40 (17): 4379–4397. https://doi.org/10.1016/S0020-7683(03)00226-9.
Collins, I. F., and T. Hilder. 2002. “A theoretical framework for constructing elastic/plastic constitutive models from triaxial tests.” Int. J. Numer. Anal Methods Geomech. 26 (13): 1313–1347. https://doi.org/10.1002/nag.247.
Collins, I. F., and G. T. Houlsby. 1997. “Application of thermomechanical principles to the modelling of geotechnical materials.” Proc. R. Soc. London 453 (1964): 1975–2001. https://doi.org/10.1098/rspa.1997.0107.
Collins, I. F., and P. Kelly. 2002. “A thermomechanical analysis of a family of soil models.” Geotechnique 52 (7): 507–518. https://doi.org/10.1680/geot.2002.52.7.507.
Collins, I. F., and B. Muhunthan. 2003. “On the relationship between stress–dilatancy, anisotropy, and plastic dissipation for granular materials.” Geotechnique 53 (7): 611–618. https://doi.org/10.1680/geot.2003.53.7.611.
Dafalias, Y., and E. Popov. 1975. “A model of nonlinearly hardening materials for complex loading.” Acta Mech. 21 (3): 173–192. https://doi.org/10.1007/BF01181053.
Farren, W., and G. Taylor. 1925. “The heat developed during plastic extension of metals.” Proc. R. Soc. London Ser. A, Containing Pap. Math. Phys. Character 107 (743): 422–451. https://doi.org/10.1098/rspa.1925.0034.
Feigenbaum, H. P., and Y. F. Dafalias. 2007. “Directional distortional hardening in metal plasticity within thermodynamics.” Int. J. Solids Struct. 44 (22-23): 7526–7542. https://doi.org/10.1016/j.ijsolstr.2007.04.025.
Jefferies, M. 1997. “Plastic work and isotropic softening in unloading.” Géotechnique 47 (5): 1037–1042. https://doi.org/10.1680/geot.1997.47.5.1037.
Jeremić, B., et al. 2019. Nonlinear finite elements: Modeling and simulation of earthquakes, soils, structures and their interaction. Davis, CA: Univ. of California.
Lee, K. L., and H. B. Seed. 1967. “Drained strength characteristics of sands.” J. Soil Mech. Foundations Div. 93 (6): 117–141.
Lubliner, J. 1990. Plasticity theory. New York: Macmillan.
Luong, M. P. 1986. “Characteristic threshold and infrared vibrothermography of sand.” Geotech. Test. J. 9 (2): 80–86. https://doi.org/10.1520/GTJ11033J.
Manzari, M. T., and Y. F. Dafalias. 1997. “A critical state two-surface plasticity model for sands.” Géotechnique 47 (2): 255–272. https://doi.org/10.1680/geot.1997.47.2.255.
Okada, N., and S. Nemat-Nasser. 1994. “Energy dissipation in inelastic flow of saturated cohesionless granular media.” Géotechnique 44 (1): 1–19. https://doi.org/10.1680/geot.1994.44.1.1.
Palmer, A. C. 1967. “Stress-strain relations for clays: An energy theory.” Géotechnique 17 (4): 348–358. https://doi.org/10.1680/geot.1967.17.4.348.
Pisanò, F., and B. Jeremić. 2014. “Simulating stiffness degradation and damping in soils via a simple visco-elastic-plastic model.” Soil Dyn. Geotech. Earthquake Eng. 63 (Aug): 98–109. https://doi.org/10.1016/j.soildyn.2014.02.014.
Rittel, D. 2000. “An investigation of the heat generated during cyclic loading of two glassy polymers. I: Experimental.” Mech. Mater. 32 (3): 131–147. https://doi.org/10.1016/S0167-6636(99)00051-4.
Rosakis, P., A. Rosakis, G. Ravichandran, and J. Hodowany. 2000. “A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals.” J. Mech. Phys. Solids 48 (3): 581–607. https://doi.org/10.1016/S0022-5096(99)00048-4.
Schofield, A., and P. Wroth. 1968. Vol. 310 of Critical state soil mechanics. London: McGraw-Hill.
Taiebat, M., and Y. F. Dafalias. 2008. “SANISAND: Simple anisotropic sand plasticity model.” Int. J. Numer. Anal. Methods Geomech. 32 (8): 915–948. https://doi.org/10.1002/nag.651.
Taylor, G. I., and H. Quinney. 1934. “The latent energy remaining in a metal after cold working.” Proc. R. Soc. London Ser. A, Containing Pap. Math. Phys. Character 143 (849): 307–326. https://doi.org/10.1098/rspa.1934.0004.
Verdugo, R., and K. Ishihara. 1996. “The steady state of sandy soils.” Soils Found. 36 (2): 81–91. https://doi.org/10.3208/sandf.36.2_81.
Veveakis, E., I. Vardoulakis, and G. Di Toro. 2007. “Thermoporomechanics of creeping landslides: The 1963 vaiont slide, northern Italy.” J. Geophys. Res. Earth Surf. 112 (F3): 1–21. https://doi.org/10.1029/2006JF000702.
Yang, H., S. K. Sinha, Y. Feng, D. B. McCallen, and B. Jeremić. 2018. “Energy dissipation analysis of elastic-plastic materials.” Comput. Methods Appl. Mech. Eng. 331 (Apr): 309–326. https://doi.org/10.1016/j.cma.2017.11.009.
Yang, H., H. Wang, Y. Feng, F. Wang, and B. Jeremić. 2019. “Energy dissipation in solids due to material inelasticity, viscous coupling, and algorithmic damping.” J. Eng. Mech. 145 (9): 1–20. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001617.
Ziegler, H., and C. Wehrli. 1987. “The derivation of constitutive relations from the free energy and the dissipation function.” Adv. Appl. Mech. 25: 183–238. https://doi.org/10.1016/S0065-2156(08)70278-3.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 146 • Issue 3 • March 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Feb 1, 2019
Accepted: Aug 6, 2019
Published online: Dec 28, 2019
Published in print: Mar 1, 2020
Discussion open until: May 28, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.