A hierarchical lattice spring model to simulate the mechanics of 2-D materials-based composites

Frontiers in Materials

Volumn 2, Issue , 2015, Pages

  Brely, Lucas ^a   Bosia, Federico ^a   Pugno, Nicola M ^b,c,d  

^a UNIVERSITY OF TURIN   (Italy)

^b UNIVERSITY OF TRENTO   (Italy)

^c FONDAZIONE BRUNO KESSLER   (Italy)

^d QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Composite materials; Fracture mechanics; Hierarchical lattice spring model; Hierarchy; Numerical modeling

Indexed keywords

BIOLOGICAL MATERIALS; COMPOSITE MATERIALS; COMPOSITE STRUCTURES; DAMAGE TOLERANCE; ENERGY DISSIPATION; FRACTURE MECHANICS; GRAPHENE; NUMERICAL MODELS; SPRINGS (COMPONENTS); STRUCTURAL PROPERTIES;

FINITE ELEMENTS SIMULATION; GEOMETRICAL NON-LINEARITY; HETEROGENEITY OF THE MATERIAL; HETEROGENEOUS STRUCTURES; HIERARCHICAL LATTICE; HIERARCHICAL STRUCTURES; HIERARCHY; LINEAR ELASTIC FRACTURE MECHANICS;

REINFORCEMENT;

EID: 84959032688     PISSN: None     EISSN: 22968016     Source Type: Journal    
DOI: 10.3389/fmats.2015.00051     Document Type: Article

References (46)

1. Absi, E., Prager, W., (1975). A comparison of equivalence and finite element methods. Comput. Methods Appl. Mech. Eng., 6, 59–64.10.1016/0045-7825(75)90015-8.
2. Alava, M. J., Nukalaz, P. K. V. V., Zapperi, S., (2006). Statistical models of fracture. Adv. Phys., 55, 349–476.10.1080/00018730300741518.
3. Ashby, M. F., Gibson, L. J., Wegst, U., Olive, R., (1995). The mechanical-properties of natural materials.1. Material property charts. Proc. R. Soc. Math. Phys. Sci., 450, 123–140.10.1098/rspa.1995.0075.
4. Banhart, F., Kotakoski, J., Krasheninnikov, A. V., (2010). Structural defects in graphene. ACS Nano, 5, 26–41.10.1021/nn102598m.
5. Bathe, K.-J. R., Bathe, K.-J. R., (1996). Finite Element Procedures. Englewood Cliffs, NJ: Prentice Hall.
6. Batoz, J.-L., Dhatt, G., (1979). Incremental displacement algorithms for nonlinear problems. Int. J. Numer. Methods Eng., 14, 1262–1267.10.1002/nme.1620140811.
7. Beale, P. D., Srolovitz, D. J., (1988). Elastic fracture in random materials. Phys. Rev. B, 37, 5500–5507.10.1103/PhysRevB.37.5500.
8. Beese, A. M., An, Z., Sarkar, S., Nathamgari, S. S. P., Espinosa, H. D., Nguyen, S. T., (2014). Defect-tolerant nanocomposites through bio-inspired stiffness modulation. Adv. Funct. Mater., 24, 2883–2891.10.1002/adfm.201303503.
9. Bigoni, D., Dal Corso, F., Gei, M., (2008). The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part II. Implications on shear band nucleation, growth and energy release rate. J. Mech. Phys. Solids, 56, 839–857.10.1016/j.jmps.2007.07.003.
10. Bosia, F., Abdalrahman, T., Pugno, N. M., (2012). Investigating the role of hierarchy on the strength of composite materials: evidence of a crucial synergy between hierarchy and material mixing. Nanoscale, 4, 1200–1207.10.1039/c2nr11664b, 22281544.
11. Bosia, F., Abdalrahman, T., Pugno, N. M., (2014). Self-healing of hierarchical materials. Langmuir, 30, 1123–1133.10.1021/la403497z, 24364755.
12. Bosia, F., Buehler, M. J., Pugno, N. M., (2010). Hierarchical simulations for the design of supertough nanofibers inspired by spider silk. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 82, 056103.10.1103/PhysRevE.82.056103, 21230541.
13. Bosia, F., Merlino, M., Pugno, N. M., (2015). Fatigue of self-healing hierarchical soft nanomaterials: the case study of the tendon in sportsmen. J. Mater. Res., 30, 2–9.10.1557/jmr.2014.335.
14. Buxton, G. A., Balazs, A. C., (2002). Lattice spring model of filled polymers and nanocomposites. J. Chem. Phys., 117, 7649–7658.10.1063/1.1509447.
15. Coleman, J. N., Khan, U., Blau, W. J., Gun’ko, Y. K., (2006). Small but strong: a review of the mechanical properties of carbon nanotube-polymer composites. Carbon N. Y., 44, 1624–1652.10.1016/j.carbon.2006.02.038.
16. Curtin, W. A., Scher, H., (1990). Brittle-fracture in disordered materials – a spring network model. J. Mater. Res., 5, 535–553.10.1557/JMR.1990.0535.
17. Dimas, L. S., Bratzel, G. H., Eylon, I., Buehler, M. J., (2013). Tough composites inspired by mineralized natural materials: computation, 3D printing, and testing. Adv. Funct. Mater., 23, 4629–4638.10.1002/adfm.201300215.
18. Friesecke, G., Theil, F., (2002). Validity and failure of the Cauchy-Born hypothesis in a two-dimensional mass-spring lattice. J. Nonlinear Sci., 12, 445–478.10.1007/s00332-002-0495-z.
19. Gao, H. J., Ji, B. H., Jager, I. L., Arzt, E., Fratzl, P., (2003). Materials become insensitive to flaws at nanoscale: lessons from nature. Proc. Natl. Acad. Sci. U.S.A., 100, 5597–5600.10.1073/pnas.0631609100, 12732735.
20. Gao, X. L., Li, K., (2005). A shear-lag model for carbon nanotube-reinforced polymer composites. Int. J. Solids Struct., 42, 1649–1667.10.1016/j.ijsolstr.2004.08.020.
21. Giesa, T., Arslan, M., Pugno, N. M., Buehler, M. J., (2011). Nanoconfinement of spider silk fibrils begets superior strength, extensibility, and toughness. Nano Lett., 11, 5038–5046.10.1021/nl203108t, 21967633.
22. Gusev, A. A., (2004). Finite element mapping for spring network representations of the mechanics of solids. Phys. Rev. Lett., 93, 034302.10.1103/PhysRevLett.93.034302, 15323824.
23. Huang, S. P., Li, Z. Y., Chen, Z., Chen, Q., Pugno, N., (2013). Study on the elastic-plastic behavior of a porous hierarchical bioscaffold used for bone regeneration. Mater. Lett., 112, 43–46.10.1016/j.matlet.2013.08.114.
24. Irwin, G. R., (1957). Analysis of stresses and strains near the end of cracking traversing a plate. J. Appl. Mech., 24, 361–364.
25. Lopez-Polin, G., Gomez-Navarro, C., Parente, V., Guinea, F., Katsnelson, M. I., Perez-Murano, F., (2015). Increasing the elastic modulus of graphene by controlled defect creation. Nat. Phys., 11, 26–31.10.1038/nphys3183.
26. Meyers, M. A., Chen, P. Y., Lin, A. Y. M., Seki, Y., (2008). Biological materials: structure and mechanical properties. Prog. Mater. Sci., 53, 1–206.10.1016/j.pmatsci.2007.05.002.
27. Meyers, M. A., Mckittrick, J., Chen, P. Y., (2013). Structural biological materials: critical mechanics-materials connections. Science, 339, 773–779.10.1126/science.1220854, 23413348.
28. Meza, L. R., Das, S., Greer, J. R., (2014). Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science, 345, 1322–1326.10.1126/science.1255908, 25214624.
29. Munch, E., Launey, M. E., Alsem, D. H., Saiz, E., Tomsia, A. P., Ritchie, R. O., (2008). Tough, bio-inspired hybrid materials. Science, 322, 1516–1520.10.1126/science.1164865, 19056979.
30. Nukala, P. K., Zapperi, S., Simunovic, S., (2005). Statistical properties of fracture in a random spring model. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 71, 066106.10.1103/PhysRevE.71.066106, 16089819.
31. Ostoja-Starzewski, M., (2002). Lattice models in micromechanics. Appl. Mech. Rev., 55, 35–60.10.1115/1.1432990.
32. Potyondy, D. O., Cundall, P. A., (2004). A bonded-particle model for rock. Int. J. Rock Mech. Min. Sci., 41, 1329–1364.10.1016/j.ijrmms.2004.09.011.
33. Puglisi, G., Truskinovsky, L., (2000). Mechanics of a discrete chain with bi-stable elements. J. Mech. Phys. Solids, 48, 1–27.10.1016/S0022-5096(99)00006-X.
34. Pugno, N. M., (2006). Mimicking nacre with super-nanotubes for producing optimized super-composites. Nanotechnology, 17, 5480–5484.10.1088/0957-4484/17/21/031.
35. Pugno, N. M., Bosia, F., Abdalrahman, T., (2012). Hierarchical fiber bundle model to investigate the complex architectures of biological materials. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 85, 011903.10.1103/PhysRevE.85.011903, 22400587.
36. Pugno, N. M., Bosia, F., Carpinteri, A., (2008). Multiscale stochastic simulations for tensile testing of nanotube-based macroscopic cables. Small, 4, 1044–1052.10.1002/smll.200800062, 18666164.
37. Pugno, N. M., Ruoff, R. S., (2004). Quantized fracture mechanics. Philos. Mag., 84, 2829–2845.10.1016/j.msec.2012.12.058, 23827605.
38. Ritchie, R. O., (2011). The conflicts between strength and toughness. Nat. Mater., 10, 817–822.10.1038/nmat3115, 22020005.
39. Sen, D., Buehler, M. J., (2011). Structural hierarchies define toughness and defect-tolerance despite simple and mechanically inferior brittle building blocks. Sci. Rep., 1, 25.10.1038/srep00035, 22355554.
40. Stankovich, S., Dikin, D. A., Dommett, G. H. B., Kohlhaas, K. M., Zimney, E. J., Stach, E. A., (2006). Graphene-based composite materials. Nature, 442, 282–286.10.1038/nature04969, 16855586.
41. Vaikhanski, L., Nutt, S. R., (2003). Fiber-reinforced composite foam from expandable PVC microspheres. Compos. Part A Appl. Sci. Manuf., 34, 1245–1253.10.1016/S1359-835X(03)00255-0.
42. Wegst, U. G. K., Bai, H., Saiz, E., Tomsia, A. P., Ritchie, R. O., (2015). Bioinspired structural materials. Nat. Mater., 14, 23–36.10.1038/nmat4089.
43. Weibull, W., (1952). A statistical distribution function of wide applicability. J. Appl. Mech., 18, 293–297.
44. Young, R. J., Kinloch, I. A., Gong, L., Novoselov, K. S., (2012). The mechanics of graphene nanocomposites: a review. Compos. Sci. Technol., 72, 1459–1476.10.1016/j.compscitech.2012.05.005, 25713442.
45. Zhang, Z. Q., Zhang, Y. W., Gao, H. J., (2011). On optimal hierarchy of load-bearing biological materials. Proc. R. Soc. B Biol. Sci., 278, 519–525.10.1098/rspb.2010.1093, 20810437.
46. Zhao, G. F., Fang, J. N., Zhao, J., (2011). A 3D distinct lattice spring model for elasticity and dynamic failure. Int. J. Numer. Anal. Methods Geomech., 35, 859–885.10.1002/nag.930.