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Lattice Spring Models

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Abstract

Solid mechanics can be addressed by a Lattice Spring Model whose major ingredients are briefly described. It is applied to solve the dynamic equations of motions and the static equations derived by homogenization. Results relative to the macroscopic properties of solids are successfully compared to the ones obtained by analytical methods and by other techniques of numerical calculations. Wave velocities derived by direct simulations are in good agreement with the ones derived by homogenization.

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References

  • Adler P.M.: Porous Media, Geometry and Transports. Butterworth-Heinemann, Stoneham (1992)

    Google Scholar 

  • Arbabi S., Sahimi M.: Test of universality for three-dimensional models of mechanical breakdown in disordered solids. Phys. Rev. B 41(1), 772–775 (1990)

    Article  Google Scholar 

  • Auriault J.L., Sanchez-Palencia E.: Etude du comportement macroscopique d’un milieu poreux saturé déformable. J. Mécanique 16(4), 575–603 (1977)

    Google Scholar 

  • Burla R.K., Kumar A.V., Sankar B.V.: Implicit boundary method for determination of effective properties of composite microstructures. Int. J. Solids Struct. 46, 2514–2526 (2009)

    Article  Google Scholar 

  • Buxton G.A., Verberg R., Jasnow D., Balazs A.C.: Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models. Phys. Rev. E 71, 056707 (2005)

    Article  Google Scholar 

  • Chung J.W., De Hosson J.Th.M., van der Giessen E.: Scaling of the failure stress of homophase and heterophase three-dimensional spring networks. Phys. Rev. B 65, 094104 (2002)

    Article  Google Scholar 

  • Grest G.S., Webman I.: Vibration properties of a percolating cluster. J. Phys. Lett. 45(24), 1155–1160 (1984)

    Article  Google Scholar 

  • Hassold G.N., Srolovitz D.J.: Brittle fracture in materials with random defects. Phys. Rev. B 39(13), 9273–9281 (1989)

    Article  Google Scholar 

  • Iwakuma T., Nemat-Nasser S.: Composites with periodic microstructure. Comput. Struct. 16(1-4), 13–19 (1983)

    Article  Google Scholar 

  • Keating P.N.: Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys. Rev. 145(2), 637–645 (1966)

    Article  Google Scholar 

  • Ladd A.J.C., Kinney J.H., Breunig T.M.: Deformation and failure in cellular materials. Phys. Rev. E. 55(3), 3271 (1997)

    Article  Google Scholar 

  • Ladd A.J.C., Kinney J.H.: Elastic constants of cellular structures. Physica A 240, 349–360 (1997)

    Article  Google Scholar 

  • Landau L.D., Lifshitz E.M.: Theory of Elasticity. Pergamon Press, Oxford (1959)

    Google Scholar 

  • Malinouskaya, I.: Propagation des ondes acoustiques dans les milieux heterogenes. Ph. D. Thesis (2007)

  • Malinouskaya I., Mourzenko V.V., Thovert J.-F., Adler P.M.: Wave propagation through saturated porous media. Phys. Rev. E 77, 066302 (2008)

    Article  Google Scholar 

  • Nunan Kevin C., Keller Joseph B.: Effective elasticity tensor of a periodic composite. J. Mech. Phys. Solids 32(4), 259–280 (1984)

    Article  Google Scholar 

  • Ostoja-Starzewski M.: Lattice models in micromechanics. Appl. Mech. Rev. 55, 35 (2002)

    Article  Google Scholar 

  • Poutet J., Manzoni D., Hage-Chehade F., Jacquin C.J., Boutéca M.J., Thovert J.-F., Adler P.M.: The effective mechanical properties of random porous media. J. Mech. Phys. Solids 44(10), 1587–1620 (1996)

    Article  Google Scholar 

  • Rodin G.J.: The overall elastic response of materials containing spherical inhomogeneities. Int. J. Solids Struct. 30(14), 1849–1863 (1993)

    Article  Google Scholar 

  • Sanchez-Palencia E.: Non homogeneous media and vibration theory. Springer-Verlag, Berlin (1980)

    Google Scholar 

  • Sangani A.S., Lu W.: Elastic coefficients of composites containing spherical inclusions in a periodic array. J. Mech. Phys. Solids 35(1), 1–21 (1987)

    Article  Google Scholar 

  • Schwartz L.M., Feng S., Thorpe M.F., Sen P.N.: Behavior of depleted elastic networks: comparison of effective-medium and numerical calculations. Phys. Rev. B. 32(7), 4607–4617 (1985)

    Article  Google Scholar 

  • Wang J.: The bond-bending model in three dimensions. J. Phys. A: Math. Gen. 22, L291–L295 (1989)

    Article  Google Scholar 

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Correspondence to P. M. Adler.

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Pazdniakou, A., Adler, P.M. Lattice Spring Models. Transp Porous Med 93, 243–262 (2012). https://doi.org/10.1007/s11242-012-9955-6

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  • DOI: https://doi.org/10.1007/s11242-012-9955-6

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