Skip to main content
SpringerLink
Log in

Fundamentals of Elastoplastic Theory

  • Chapter
  • First Online:
Practice of Constitutive Modelling for Saturated Soils

  • 843 Accesses

Abstract

This chapter presents the classic constitutive modeling method known as the conventional elastoplastic theory with different components, such as the elastic stress–strain relationship, the elastoplastic relationship, which includes the yield surface, flow rule, and hardening rule, and Drucker’s stability hypothesis, convexity, and orthogonality. Some typical numerical methods for solving plastic problems are also presented, such as the general explicit solution, the cutting plane method-based implicit solution, and the closest point projection method-based implicit solution.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Roscoe KH, Burland J (1968) On the generalized stress-strain behaviour of wet clay. Paper presented at the Engineering Plasticity, Cambridge, UK

    MATH  Google Scholar 

  2. Richart F, Hall J, Woods R (1970) Vibrations of soils and foundations. International Series in Theoretical and Applied Mechanics. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  3. Hardin BO, Black WL (1966) Sand stiffness under various triaxial stresses. Journal of Soil Mechanics & Foundations Div 92 (ASCE# 4712 Proceeding)

    Google Scholar 

  4. Brinkgreve R, Swolfs W, Engin E, Waterman D, Chesaru A, Bonnier P, Galavi V (2010) PLAXIS 2D 2010. User manual, Plaxis bv

    Google Scholar 

  5. Graham J, Houlsby G (1983) Anisotropic elasticity of a natural clay. Geotechnique 33(2):165–180

    Google Scholar 

  6. Yin Z-Y, Jin Y-F, Shen S-L, Huang H-W (2017) An efficient optimization method for identifying parameters of soft structured clay by an enhanced genetic algorithm and elastic–viscoplastic model. Acta Geotech 12(4):849–867. https://doi.org/10.1007/s11440-016-0486-0

    Article  Google Scholar 

  7. Chen H, Yu T, Wang X, Liu Z (2005) Elasticity and plasticity. China Architecture & Building Press,

    Google Scholar 

  8. Luo T, Yao Y (2010) Constitutive relationship of soil. Beijing: China Communications Press

    Google Scholar 

  9. Zhang F (2007) Computational Soil Mechanics. Beijing: China Communications Press

    Google Scholar 

  10. Roscoe K, Schofield A, Thurairajah A (1963) Yielding of clays in states wetter than critical. Geotechnique 13(3):211–240

    Google Scholar 

  11. Roscoe K, Schofield AN, Wroth C (1958) On the yielding of soils. Geotechnique 8(1):22–53

    Google Scholar 

  12. Schofield A, Wroth P (1968) Critical state soil mechanics

    Google Scholar 

  13. Dafalias YF (1986) An anisotropic critical state soil plasticity model. Mech Res Commun 13(6):341–347

    MATH  Google Scholar 

  14. Ling HI, Yue D, Kaliakin VN, Themelis NJ (2002) Anisotropic elastoplastic bounding surface model for cohesive soils. Journal of engineering mechanics 128(7):748–758

    Google Scholar 

  15. Drucker DC (1960) On structural concrete and the theorems of limit analysis. Brown University, Division of Engineering

    Google Scholar 

  16. Yu H-S (2007) Plasticity and geotechnics, vol 13. Springer Science & Business Media,

    Google Scholar 

  17. Koiter WT (1953) Stress-strain relations, uniqueness and variational theorems for elastic- plastic materials with a singular yield surface. Q Appl Math 11(3):350–354

    Google Scholar 

  18. Ortiz M, Simo J (1986) An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int J Numer Methods Eng 23(3):353–366

    MathSciNet  MATH  Google Scholar 

  19. Simo J, Taylor R (1986) A return mapping algorithm for plane stress elastoplasticity. Int J Numer Methods Eng 22(3):649–670

    MathSciNet  MATH  Google Scholar 

  20. Lade PV, Duncan JM (1975) Elastoplastic stress-strain theory for cohesionless soil. Journal of Geotechnical and Geoenvironmental Engineering 101 (ASCE# 11670 Proceeding)

    Google Scholar 

  21. Matsuoka H, Nakai T (1985) Relationship among tresca, mises, mohr-coulomb and matsuoka-nakai failure criteria. Soils Found 25(4):123–128

    Google Scholar 

  22. Yao Y, Lu D, Zhou A, Zou B (2004) Generalized non-linear strength theory and transformed stress space. Sci China Ser E: Technol Sci 47(6):691–709

    MATH  Google Scholar 

  23. Sheng D, Sloan S, Yu H (2000) Aspects of finite element implementation of critical state models. Comput Mech 26(2):185–196

    MATH  Google Scholar 

  24. Argyris J, Faust G, Szimmat J, Warnke E, Willam K (1974) Recent developments in the finite element analysis of prestressed concrete reactor vessels. Nucl Eng Des 28(1):42–75

    Google Scholar 

  25. Satake M Fabric tensor in granular materials. In: IUTAM Conference on Deformation and Flow of Granular Materials, 1982, 1982. AA Balkema, pp 63–68

    Google Scholar 

  26. Zheng Y (2000) Theory of generalized plastic mechanics. Rock Soil Mech 21(2):188–192

    Google Scholar 

  27. Nakai T, Matsuoka H (1986) A generalized elastoplastic constitutive model for clay in three-dimensional stresses. Soils Found 26(3):81–98

    Google Scholar 

  28. Yao Y-P, Zhou A-N, Lu D-C (2007) Extended transformed stress space for geomaterials and its application. Journal of engineering mechanics 133(10):1115–1123

    Google Scholar 

  29. Whittle AJ, Kavvadas MJ (1994) Formulation of MIT-E3 constitutive model for overconsolidated clays. Journal of geotechnical engineering 120(1):173–198

    Google Scholar 

  30. Chowdhury E, Nakai T (1998) Consequences of the tij-concept and a new modeling approach. Comput Geotech 23(3):131–164

    Google Scholar 

  31. Borja RI, Lin C-H, Montáns FJ (2001) Cam-Clay plasticity, Part IV: Implicit integration of anisotropic bounding surface model with nonlinear hyperelasticity and ellipsoidal loading function. Comput Methods Appl Mech Eng 190(26–27):3293–3323

    MATH  Google Scholar 

  32. Cudny M, Vermeer PA (2004) On the modelling of anisotropy and destructuration of soft clays within the multi-laminate framework. Comput Geotech 31(1):1–22

    Google Scholar 

  33. Gens A, Nova R (1993) Conceptual bases for a constitutive model for bonded soils and weak rocks. Geotechnical engineering of hard soils-soft rocks 1(1):485–494

    Google Scholar 

  34. Lagioia R, Puzrin A, Potts D (1996) A new versatile expression for yield and plastic potential surfaces. Comput Geotech 19(3):171–191

    Google Scholar 

  35. Yu H (1998) CASM: A unified state parameter model for clay and sand. Int J Numer Anal Methods Geomech 22(8):621–653

    MATH  Google Scholar 

  36. Bardet J-P (1986) Bounding surface plasticity model for sands. Journal of engineering mechanics 112(11):1198–1217

    Google Scholar 

  37. Crouch RS, Wolf JP, Dafalias YF (1994) Unified critical-state bounding-surface plasticity model for soil. Journal of engineering mechanics 120(11):2251–2270

    Google Scholar 

  38. Anandarajah A An anisotropic hardening bounding surface constitutive model for clays. In: Proc. 5th Int. Conf. Num. Meth. Geomech., 1985. pp 267–275

    Google Scholar 

  39. Mróz Z, Boukpeti N, Drescher A (2003) Constitutive model for static liquefaction. Int J Geomech 3(2):133–144

    Google Scholar 

  40. Jefferies M (1993) Nor-Sand: a simple critical state model for sand. Geotechnique 43(1):91–103

    Google Scholar 

  41. Yao Y, Liu L, Luo T (2018) A constitutive model for granular soils. Science China Technological Sciences 61(10):1546–1555. https://doi.org/10.1007/s11431-017-9205-8

    Article  Google Scholar 

  42. McDowell G (2002) A simple non-associated flow model for sand. Granular Matter 4(2):65–69

    Google Scholar 

  43. McDowell G, Hau K (2004) A generalised Modified Cam clay model for clay and sand incorporating kinematic hardening and bounding surface plasticity. Granular Matter 6(1):11–16

    MATH  Google Scholar 

  44. Rowe PW, Rowe P (1962) The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proc R Soc Lond A 269(1339):500–527

    Google Scholar 

  45. Gajo A, Wood M (1999) Severn-Trent sand: a kinematic-hardening constitutive model: the q–p formulation. Geotechnique 49(5):595–614

    Google Scholar 

  46. Yang C, Sheng D, Carter JP, Sloan SW (2015) Modelling the plastic anisotropy of Lower Cromer Till. Comput Geotech 69:22–37

    Google Scholar 

  47. Dafalias Y, Taiebat M (2013) Anatomy of rotational hardening in clay plasticity. Géotechnique 63(16):1406

    Google Scholar 

  48. Wheeler SJ, Näätänen A, Karstunen M, Lojander M (2003) An anisotropic elastoplastic model for soft clays. Can Geotech J 40(2):403–418

    Google Scholar 

  49. Cudny M, Zentar R, Abriak N-E Two approaches to model the behaviour of soft natural clays under principal stress axes rotation. In: Proceedings of the 9th International Symposium on Numerical Models in Geomechanics (NUMOG IX), 2004. pp 145–151

    Google Scholar 

  50. Nova R (1988) Sinfonietta classica: an exercise on classical soil modelling. Constitutive Equations for Granular non-cohesive soils:501–519

    Google Scholar 

  51. Rouainia M, Muir Wood D (2000) A kinematic hardening constitutive model for natural clays with loss of structure. Géotechnique 50(2):153–164

    Google Scholar 

  52. Nova R (1977) Hardening of soils. Archives of Mechanics 29(3):445–458

    Google Scholar 

  53. Nova R (1992) Mathematical modelling of natural and engineered geomaterials. General lecture 1st ECSM Munchen. Eur J Mech A/Solids 11:135–154

    Google Scholar 

  54. Yao Y, Sun D, Matsuoka H (2008) A unified constitutive model for both clay and sand with hardening parameter independent on stress path. Comput Geotech 35(2):210–222

    Google Scholar 

  55. Kavvadas M, Amorosi A (2000) A constitutive model for structured soils. Geotechnique 50(3):263–274

    Google Scholar 

  56. Baudet B, Stallebrass S (2004) A constitutive model for structured clays. Géotechnique 54(4):269–278

    Google Scholar 

  57. Callisto L, Gajo A, Muir Wood D (2002) Simulation of triaxial and true triaxial tests on natural and reconstituted Pisa clay. Géotechnique 52(9):649–666

    Google Scholar 

  58. Anandarajah A (1994) Procedures for elastoplastic liquefaction modeling of sands. Journal of engineering mechanics 120(7):1563–1589

    Google Scholar 

  59. Manzari MT, Dafalias YF (1997) A critical state two-surface plasticity model for sands. Geotechnique 47(2):255–272

    Google Scholar 

  60. Alshamrani MA, Sture S (1998) A time-dependent bounding surface model for anisotropic cohesive soils. Soils Found 38(1):61–76

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China

    Prof. Zhen-Yu Yin

  2. Research Institute in Civil and Mechanical Engineering UMR CNRS GeM, Ecole Centrale de Nantes, Nantes, France

    Pierre-Yves Hicher

  3. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China

    Yin-Fu Jin

Authors
  1. Prof. Zhen-Yu Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pierre-Yves Hicher
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yin-Fu Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhen-Yu Yin .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd. and Tongji University Press

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Yin, ZY., Hicher, PY., Jin, YF. (2020). Fundamentals of Elastoplastic Theory. In: Practice of Constitutive Modelling for Saturated Soils. Springer, Singapore. https://doi.org/10.1007/978-981-15-6307-2_4

Download citation

Publish with us

Policies and ethics

Search

Navigation