Experimental Mechanics

, Volume 57, Issue 7, pp 1091–1105 | Cite as

Numerical Modeling of Elastic Spherical Contact for Mohr-Coulomb Type Failures in Micro-Geomaterials

  • Y. HanEmail author
  • Y.N. Abousleiman
  • K.L. Hull
  • G.A. Al-Muntasheri


The contact behavior for geological materials, such as reservoir shale rock, is simulated using the finite element method by considering a nano-indenter tip indenting into a geomaterial obeying the Mohr-Coulomb failure criterion. The deformation and slip at the micro-scale along the shear direction in grain-to-grain contact follows the Coulomb frictional/sliding failure criterion, while the linear elastic force-displacement law is enforced in the direction normal to the contact surface. A series of simulations are performed to study the effect of cohesion, friction angle, and tensile strength on the contact response. For a material with very high cohesion and frictionless contact, the indented geomaterial behaves almost purely as an elastic medium. In this case, the indentation process converges to the classic Hertz grain-to-grain spherical contact model. For a material with extremely low cohesion, the geomaterial behaves like cohesionless granular material at the micro-scale. For materials with finite cohesion values, such as shales, the force-displacement responses are analyzed and reported. This simulation is compared to micro-indentation tests using a spherical indenter tip conducted on preserved samples of Woodford shale.


Nanoindentation Hertz contact Stiffness and strength Shale Force-deformation curve 



The authors wish to thank Saudi Aramco and Aramco Services Company for permission to publish this research work.


  1. 1.
    Han Y, Al-Muntasheri G, Hull K, Abousleiman Y (2016) Tensile mechanical behavior of Kerogen and its potential implication to fracture opening in Kerogen-Rich Shales (KRS). ARMA 16–86. Presented at the 50th US Rock Mechanics / Geomechanics Symposium held in Houston, Texas, USA, 26–29 June 2016Google Scholar
  2. 2.
    Goodman RE (1989) Introduction to rock mechanics, Vol. 2. Wiley, New YorkGoogle Scholar
  3. 3.
    Santarelli FJ, Marsala AF, Brignoli M, Rossi E, Bona A (1998) Formation evaluation from logging on cuttings. SPE Reserv Eval Eng 1.03:238–244Google Scholar
  4. 4.
    Abousleiman Y, Hoang SK, Tran MH (2010) Mechanical characterization of small shale samples subjected to fluid using the inclined direct shear testing device. Int J Rock Mech Min Sci 47:355–367CrossRefGoogle Scholar
  5. 5.
    Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 19:3–20CrossRefGoogle Scholar
  6. 6.
    Charleux L, Gravier S, Verdier M, Fivel M, Blandin JJ (2007) Indentation plasticity of amorphous and partially crystallized metallic glasses. J Mater Res 22(2):525–532CrossRefGoogle Scholar
  7. 7.
    Ganneau FP, Constantinides G, Ulm F-J (2006) Dual-indentation technique for the assessment of strength properties of cohesive-frictional materials. Int J Solids Struct 43(6):1727–1745CrossRefzbMATHGoogle Scholar
  8. 8.
    Liu M, Lu C, Tieu K, Peng C, Kong C (2015) A combined experimental-numerical approach for determining mechanical properties of aluminum subjects to Nanoindentation. Sci Report 5:17072. doi: 10.1038/srep15072 CrossRefGoogle Scholar
  9. 9.
    Rodríguez M, Molina-Aldareguía JM, González C, LLorca J (2012) Determination of the mechanical properties of amorphous materials through instrumented nanoindentation. Acta Mater 60(9):3953–3964CrossRefGoogle Scholar
  10. 10.
    Sarris E, Constantinides G (2013) Finite element modeling of nanoindentation on C-S-H: effect of pile-up and contact friction. Cem Concr Compos 36:78–84CrossRefGoogle Scholar
  11. 11.
    Seltzer R, Cisilino AP, Frontini PM, Mai Y (2011) Determination of the Drucker-Prager parameters of polymers exhibiting pressure-sensitive plastic behaviour by depth-sensing indentation. Int J Mech Sci 53(6):471–478CrossRefGoogle Scholar
  12. 12.
    Vaidyanathan R, Dao M, Ravichandran G, Suresh S (2001) Study of mechanical deformation in bulk metallic glass through instrumented indentation. Acta Mater 49(18):3781–3789CrossRefGoogle Scholar
  13. 13.
    Wang X, Allen MR, Burr DB, Lavernia EJ, Jeremić B, Fyhrie DP (2008) Identification of material parameters based on Mohr-Coulomb failure criterion for bisphosphonate treated canine vertebral cancellous bone. Bone 43(4):775–780CrossRefGoogle Scholar
  14. 14.
    Abousleiman Y, Hull KL, Han Y, Al-Muntasheri GA, Hosemann G, Parker SS, Howard CB (2016) The granular and polymer nature of Kerogen rich shale. Acta Geotech 11(3):573–594CrossRefGoogle Scholar
  15. 15.
    Hull KL, Abousleiman YN, Han Y, Al-Muntasheri GA, Hosemann P, Parker SS, Howard CB (2015) New insights on the mechanical characterization of Kerogen-rich shale, KRS. SPE-177628. Presented at the Abu Dhabi international petroleum exhibition and conference held in Abu Dhabi, UAE, 9-12 November 2015Google Scholar
  16. 16.
    Johnson KL (1987) Contact mechanics. University Press, CambridgeGoogle Scholar
  17. 17.
    Timoshenko S, Goodier JN (1951) Theory of elasticity. McGraw-Hill Book Company, New YorkzbMATHGoogle Scholar
  18. 18.
    Hertz HR (1882) Ueber die Beruehrung elastischer Koerper (on contact between elastic bodies), in Gesammelte Werke (collected works), Vol. 1, Leipzig, Germany, 1895Google Scholar
  19. 19.
    Cundall PA (2011) Fast Lagrangian analysis of continua, Version 7.0. Itasca Consulting Group, Inc, Minneapolis, MinnesotaGoogle Scholar
  20. 20.
    Rummel F, Fairhurst C (1970) Determination of the post-failure behavior of brittle rock using a servo-controlled testing machine. Rock Mech 2:189–204CrossRefGoogle Scholar
  21. 21.
    Liu Y, Wang B, Yoshino M, Roy S, Lu H, Komanduri R (2005) Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale. J Mech Phys Solids 53:2718–2741CrossRefzbMATHGoogle Scholar
  22. 22.
    Chen Z, Wang X, Atkinson A, Brandon N (2016) Spherical indentation of porous ceramics: elasticity and hardness. J Eur Ceram Soc 36(6):1435–1445CrossRefGoogle Scholar
  23. 23.
    Oliver WC, McHargue CJ, Farlow GC, White CW (1985) The hardness of ion implanted ceramics. Mater Res Soc Symp Proc 60:515Google Scholar
  24. 24.
    Suresh S, Nieh T-G, Choi BW (1999) Nano-indentation of copper thin films on silicon substrates. Scr Mater 41:951–957CrossRefGoogle Scholar
  25. 25.
    Hull K, Abousleiman YN (2017) Pop-ins observations and analysis in geological organic-rich shale. In PreparationGoogle Scholar
  26. 26.
    Ortega A, Ulm F-J, Abousleiman Y (2009) The Nanogranular acoustic signature of shale. Geophysics 74(3):65–84CrossRefGoogle Scholar
  27. 27.
    Ulm F-J, Abousleiman Y (2006) The granular nature of shale. Acta Geotech 1(1):77–88CrossRefGoogle Scholar
  28. 28.
    Bennett KC, Berla LA, Nix WD, Borja RI (2015) Instrumented Nanoindentation and 3D mechanistic modeling of a shale at multiple scales. Acta Geotech 10:1–14CrossRefGoogle Scholar
  29. 29.
    Alkorta J, Martínez-Esnaola JM, Sevillano JG (2008) Critical examination of strain-rate sensitivity measurement by nanoindentation methods: application to severely deformed niobium. Acta Mater 56(4):884–893CrossRefGoogle Scholar
  30. 30.
    Alsalman ME, Myers MT, Sharf-Aldin MH (2015) Comparison of multistate to singlestage triaxial tests. Presented at the 49th US Rock Mechanics / Geomechanics Symposium held in San Francisco, CA, USA, 28 June – 1 July 2015. ARMA 15–767Google Scholar

Copyright information

© Society for Experimental Mechanics 2017

Authors and Affiliations

  • Y. Han
    • 1
    Email author
  • Y.N. Abousleiman
    • 2
  • K.L. Hull
    • 1
  • G.A. Al-Muntasheri
    • 1
  1. 1.Aramco Services Company: Aramco Research Center – HoustonHoustonUSA
  2. 2.Integrated PoroMechanics Institute, Mewbourne School of Petroleum and Geological EngineeringThe University of OklahomaNormanUSA

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