Computational Particle Mechanics

, Volume 5, Issue 2, pp 191–201 | Cite as

Discrete element modeling of microstructure of nacre

  • Mei Qiang Chandler
  • Jing-Ru C. Cheng


The microstructure of nacre consists of polygon-shaped aragonite mineral tablets bonded by very thin layers of organic materials and is organized in a brick–mortar morphology. In this research, the discrete element method was utilized to model this structure. The aragonite mineral tablets were modeled with three-dimensional polygon particles generated by the Voronoi tessellation method to represent the Voronoi-like patterns of mineral tablets assembly observed in experiments. The organic matrix was modeled with a group of spring elements. The constitutive relations of the spring elements were inspired from the experimental results of organic molecules from the literature. The mineral bridges were modeled with simple elastic bonds with the parameters based on experimental data from the literature. The bulk stress–strain responses from the models agreed well with experimental results. The model results show that the mineral bridges play important roles in providing the stiffness and yield strength for the nacre, while the organic matrix in providing the ductility for the nacre. This work demonstrated the suitability of particle methods for modeling microstructures of nacre.


Discrete element method Nacre Microstructure Material modeling 



The authors acknowledge the financial support for this work provided by the US Army Engineer Research and Development Center (ERDC) Military Engineering 6.1 Basic Research Program. Permission to publish was granted by the Director, ERDC Geotechnical and Structures Laboratory.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. 1.
    Wang RZ, Suo Z, Evans AG, Yao N, Aksay IA (2001) Deformation mechanisms in nacre. J Mater Res 16(9):2485–2493CrossRefGoogle Scholar
  2. 2.
    Barthelat F, Tang H, Zavattieri PD, Li CM, Espinosa HD (2007) On the mechanics of mother-of-pearl: a key feature in the material hierarchical structure. J Mech Phys Solids 55:306–337CrossRefGoogle Scholar
  3. 3.
    Schenk AS, Kim YY (2015) Unraveling the internal microstructure of biogenic and bioinspired calcite single crystals. MRS Bull 40(6):499–508CrossRefGoogle Scholar
  4. 4.
    Allison PG, Chandler MQ, Rodriguez RI, Williams BA, Moser RD, Weiss CA, Kennedy AJ, Poda AR, Lafferty BJ, Seiter JM, Hodo WD, Cook RF (2013) Mechanical properties and structure of the biological multilayered material system, Atractosteus spatula scales. Acta Biomater 9(2):5280–5288CrossRefGoogle Scholar
  5. 5.
    Allison PG, Rodriguez RI, Moser RD, Williams BA, Poda AR, Seiter JM, Lafferty BJ, Kennedy AJ, Chandler MQ (2014) Characterization of multi-layered fish scales (Atractosteus spatula) using nanoindentation, X-ray CT, FTIR, and SEM. J Video Exper 89:1–9Google Scholar
  6. 6.
    Bruet BJF, Song J, Boyce MC, Ortiz C (2008) Materials design principals of ancient fish armour. Nat Mater 7(9):748–756CrossRefGoogle Scholar
  7. 7.
    Yang W, Gludovatz B, Zimmermann EA, Bale HA (2013) Structure and fracture resistance of alligator gar (Atractosteus spatula). Acta Biomater 9:5876–5889CrossRefGoogle Scholar
  8. 8.
    Tang H, Barthelat F, Espinosa HD (2007) An elasto-viscoplastic interface model for investigating the constitutive behavior of nacre. J Mech Phys Solids 55:1410–1438CrossRefzbMATHGoogle Scholar
  9. 9.
    Han L, Wang J, Song J, Boyce MC, Ortiz C (2011) Direct quantification of the mechanical anisotropy and fracture of an individual exoskeleton layer via uniaxial compression of micropillars. Nano Lett 11(9):3868–3874CrossRefGoogle Scholar
  10. 10.
    Chandler MQ, Allison PG, Rodriguez RI, Moser RD, Kennedy AJ (2014) Finite element modeling of multilayered structures of fish scales. J Mech Behav Biomed Mater 40:375–389CrossRefGoogle Scholar
  11. 11.
    Katti K, Katti DR, Tang J, Pradhan S (2005) Modeling mechanical responses in a laminated biocomposite. J Mater Sci 40:1749–1755Google Scholar
  12. 12.
    Qi HJ, Bruet BJF, Palmer JS, Ortiz C, Boyce MC (2005) Micromechanics and macromechanics of the tensile deformation of nacre. In: Holzapfel GA, Ogden RW (eds) Mechanics of biological tissues. Springer, Berlin, pp 175–189Google Scholar
  13. 13.
    Kumar P, Nukala VV, Šimunović S (2005) Statistical physics models for nacre fracture simulation. Phys Rev E 72(041919):1–9Google Scholar
  14. 14.
    Gao H, Ji IL, Arzt E, Fratzl P (2003) Materials become insensitive to flaws at nanoscale: lessons from nature. Proc Natl Acad Sci USA 100:5597–5600CrossRefGoogle Scholar
  15. 15.
    Anandarajah A (1994) Discrete element method for simulating behavior of cohesive soil. J Geotech Eng 120(9):1593–1613CrossRefGoogle Scholar
  16. 16.
    Yao M, Anandarajah A (2003) Three-dimensional discrete element method of analysis of clays. J Eng Mech ASCE 129(6):585–596CrossRefGoogle Scholar
  17. 17.
    Chandler MQ, Peters JF, Pelessone D (2010) Modeling nanoindentation of calcium-silicate-hydrate. J Transp Res Board 2:7Google Scholar
  18. 18.
    Chandler MQ, Peters JF, Pelessone D (2013) Discrete element modeling of calcium-silicate-hydrate. Model Simul Mater Sci Eng 21(5):055010CrossRefGoogle Scholar
  19. 19.
    Parratt K, Yao JM, Poirier GR, Yao N (2014) Plasma-etching of the organic layer in nacre. Soft Nanosci Lett 4:63–68CrossRefGoogle Scholar
  20. 20.
    Smith BL, SchaÈffer IE, Viani M, Thompson JB, Frederick NA, Kindt J, Belcher A, Stucky GD, Morse DE, Morse PK (1999) Molecular mechanistic origin of the toughness of natural adhesives, fibers and composites. Nature 399(24):761–763CrossRefGoogle Scholar
  21. 21.
    Song F, Soh AK, Bai YL (2003) Structural and mechanical properties of the organic matrix layers of nacre. Biomaterials 24:9CrossRefGoogle Scholar
  22. 22.
    Lopez MI, Martinez PEM, Meyers MA (2014) Organic interlamellar layers, mesolayers and mineral nanobridges: contribution to strength in abalone (Haliotis rufescence) nacre. Acta Biomater 10:2056–2064CrossRefGoogle Scholar
  23. 23.
    Hopkins MA (2004) Discrete element modeling with dilated particles. Eng Comput 21(2/3/4):422–430CrossRefzbMATHGoogle Scholar
  24. 24.
    Knuth MA, Johnson JB, Hopkins MA, Sullivan RJ, Moore JM (2012) Discrete element modeling of a Mars Exploration Rover wheel in granular material. J Terramech 49:27–36CrossRefGoogle Scholar
  25. 25.
    Hopkins MA, Thorndike AS (2006) Floe formation in Arctic sea ice. J Geophys Res 111(C11S23):1–9Google Scholar
  26. 26.
    Hansma PG, Fantne KJH, Thurner PJ, Schitte G, Turner PJ, Udwin SF, Finch MM (2005) Sacrificial bonds in the interfibrillar matrix of bone. J Musculoskelet Neuronal Interact 5(4):313–315Google Scholar
  27. 27.
    Sumitomo T, Kakisawa H, Owaki Y, Kagawa Y (2008) In situ transmission electron microscopy observation of reversible deformation in nacre organic matrix. J Mater Res 23(5):1466–1471CrossRefGoogle Scholar
  28. 28.
    Lopez MI, Chen PY, McKittrick J, Meyers MA (2011) Growth of nacre in abalone: seasonal and feeding effects. Mater Sci Eng C 31(4):716–723CrossRefGoogle Scholar
  29. 29.
    Meyers MA, Lin AYM, Chen PY, Muyco J (2008) Mechanical strength of abalone nacre: role of the soft organic layer. J Mech Behav Biomed Mater 1(1):76–85CrossRefGoogle Scholar

Copyright information

© OWZ (outside the USA) 2017

Authors and Affiliations

  1. 1.U.S. Army Engineer Research and Development CenterVicksburgUSA

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