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Nonexistence and non-decoupling of the dissipative potential for geo-materials

  • Received : 2015.04.04
  • Accepted : 2015.05.20
  • Published : 2015.11.25

Abstract

Two fundamental issues exist in the damage theory of geo-material based on the concept of thermodynamics: existence or nonexistence of the dissipation potential, and whether the dissipation potential could be decoupled into a damage potential and a plastic one or not. Thermodynamics theory of elastoplastic damage assumes the existence of dissipation potential, but the presence of dissipation potential is conditional. Based on the dissipation inequality in accord with the second law of thermodynamics, the sufficient and necessary conditions are given for the existence of the dissipation potential separately in total and incremental forms firstly, and proved strictly in theory. With taking advantage of the basic mechanical properties of geo-materials, the nonexistence of the dissipative potential is verified. The sufficient and necessary conditions are also given and proved for the decoupling of the dissipation potential of geo-materials in total and incremental forms. Similarly, the non-decoupling of the dissipation potential has also been proved, which indicates the dissipation potential of geo-materials in total or incremental forms could not be decoupled into a dissipative potential for plasticity and that for damage respectively. The research results for the fundamental issues in the thermodynamics theory of damage will help establish and improve the theoretic basis of elastoplastic damage constitutive model for geo-materials.

Keywords

geo-material;constitutive relation;thermodynamics;damage;dissipative potential;decoupling

References

  1. Anandarajah, A., Sobhan, K. and Kuganenthira, N. (1995), "Incremental stress-strain behavior of granular soils", J. Geomech. Eng., 121(1), 57-67.
  2. Faria, R., Oliver, J. and Ceverra, M. (1998). "A strain-based plastic viscous-damage model for massive concrete structures", Int. J. Solid. Struct., 35(14), 1533-1558. https://doi.org/10.1016/S0020-7683(97)00119-4
  3. Guo, X., Zhao, C.G., Yuan, D.J. and Wang, M.S. (2008), "A dual-surface damage model and evaluation for natural soils within the thermomechanical framework", Acta Mechanica Solida Sinica, 21(1), 85-94. https://doi.org/10.1007/s10338-008-0811-8
  4. Houlsby, G.T. and Puzrin, A.M. (2000), "A thermomechanical framework for constitutive models for rate-independent dissipative materials", Int. J. Plasticity, 16(9), 1017-1047. https://doi.org/10.1016/S0749-6419(99)00073-X
  5. Huang, Z.P. (2003), Foundamentals of Continuum Mechanics, Higher Education Press, Beijing, China. [In Chinese]
  6. Kavvadas, M. and Amorosi, A. (2000), "A constitutive model for structured soils", Geotechnique, 50(3), 263-274. https://doi.org/10.1680/geot.2000.50.3.263
  7. Krajcinovic, D. (1985), "Continuum damage mechanics revisited: Basic concepts and definitions", J. Appl. Mech., 52(4), 829-834. https://doi.org/10.1115/1.3169154
  8. Krajcinovic, D. (1989), "Damage mechanics", Mech. Mater., 8(2-3), 117-197. https://doi.org/10.1016/0167-6636(89)90011-2
  9. Lagioia, R. and Nova, R. (1995), "An experimental and theoretical study of the behavior of a calcarenite in triaxial compression", Geotechnique, 45(4), 633-648. https://doi.org/10.1680/geot.1995.45.4.633
  10. Lai, Y.M., Jin, L. and Chang, X.X. (2009), "Yield criterion and elasto-plastic damage constitutive model for frozen sandy soil", Int. J. Plasticity, 25(6), 1177-1205. https://doi.org/10.1016/j.ijplas.2008.06.010
  11. Lemaitre, J. (1985), "Coupled elasto-plasticity and damage constitutive equations", Comput. Method. Appl. Mech. Eng., 51(1-3), 31-49. https://doi.org/10.1016/0045-7825(85)90026-X
  12. Lemaitre, J. and Chaboche, J.L. (1990), Mechanics of Solid Materials, Cambridge University Press, Cambridge, UK.
  13. Liu, Y.X., Zhou, J.W., Li, Z.Y., Chen, C. and Zheng, Y.R. (2009), "Several basic problems in plastic theory of geomaterials", Frontier of Architecture and Civil Engineering in China, 3(1), 81-84. https://doi.org/10.1007/s11709-009-0016-3
  14. Loredana, C. and Massimo, C. (2002), "A new thermodynamically consistent continuum model for hardening plasticity coupled with damage", Int. J. Solid. Struct., 39(25), 6241-6271. https://doi.org/10.1016/S0020-7683(02)00470-5
  15. Lu, W.B., Hu, Y.G., Yang, J.H., Chen, M. and Yan, P. (2013), "Spatial distribution of excavation induced damage zone of high rock slope", Int. J. Rock Mech. Min. Sci., 64, 181-191.
  16. Mortazavi, A. and Molladavoodi, H. (2012), "A numerical investigation of brittle rock damage model in deep underground openings", Eng. Fract. Mech., 90, 101-120. https://doi.org/10.1016/j.engfracmech.2012.04.024
  17. Nguyen, G.D. (2005), "A thermodynamic approach to constitutive modeling of concrete using damage mechanics and plasticity theory", Ph.D. Dissertation; Oxford University, Oxford, UK.
  18. Nguyen, G.D. and Houlsby, G.T. (2004), "A thermodynamic approach to constitutive modeling of concrete", Proceedings of the 12th Conference of Association for Computational Mechanics in Engineering (ACME-UK), Cardiff, UK, April.
  19. Salari, M.R., Saeb, S., Willam, K.J., Patchet, S.J. and Carrasco, R.C. (2004), "A coupled elastoplastic damage model for geomaterials", Comput. Meth. Appl. Mech. Eng., 193(27-29), 2625-2643. https://doi.org/10.1016/j.cma.2003.11.013
  20. Shao, J.F., Ata, N. and Ozanam, O. (2005), "Study of desaturation and resaturation in brittle rock with anisotropic damage", Eng. Geol., 81(3), 341-352. https://doi.org/10.1016/j.enggeo.2005.06.015
  21. Shao, J.F., Jia, Y., Kondo, D. and Chiarelli, A.S. (2006), "A coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions", Mech. Mater., 38(3), 218-232. https://doi.org/10.1016/j.mechmat.2005.07.002
  22. Shojaei, A., Taleghani, A.D. and Li, G.Q. (2014), "A continuum damage failure model for hydraulic fracturing of porous rocks", Int. J. Plasticity, 59, 199-212. https://doi.org/10.1016/j.ijplas.2014.03.003
  23. Voyiadjis, G.Z. and Kattan, P.I. (1990), "A coupled theory of damage mechanics and finite strain elasto-plasticity-II, damage and finite strain plasticity", Int. J. Eng. Sci., 28(6), 505-524. https://doi.org/10.1016/0020-7225(90)90053-L
  24. Voyiadjis, G.Z. and Kattan, P.I. (1992), "A plasticity-damage theory for large deformation of solids - part I: Theoretical formulation", Int. J. Eng. Sci., 30(9), 1089-1108. https://doi.org/10.1016/0020-7225(92)90059-P
  25. Voyiadjis, G.Z., Shojaei, A. and Li, G.Q. (2011), "A thermodynamic consistent damage and healing model for self healing materials", Int. J. Plast., 27(7), 1025-1044. https://doi.org/10.1016/j.ijplas.2010.11.002
  26. Zhou, J.T. and Liu, Y.X. (2007), "Constitutive model for isotropic damage of geomaterial", Chinese J. Geotech. Eng., 29(11), 1636-1641. [In Chinese]
  27. Zhou, H., Bian, H.B., Jia, Y. and Shao, J.F. (2013), "Elastoplastic damage modeling the mechanical behavior of rock-like materials considering confining pressure dependency", Mech. Res. Commun., 53, 1-8. https://doi.org/10.1016/j.mechrescom.2013.07.008
  28. Zhu, Z.W., Ning, J.G. and Song, S.C. (2010), "Finite-element simulations of a road embankment based on a constitutive model for frozen soil with the incorporation of damage", Cold Regions Sci. Technol., 62(2-3), 151-159. https://doi.org/10.1016/j.coldregions.2010.03.010

Acknowledgement

Supported by : National Natural Science Foundation of China, Chongqing Natural Science Foundation