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One-Dimensional Microelasticity

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Internal Variables in Thermoelasticity

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 243))

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Abstract

It is demonstrated on the example of one-dimensional elastic pulse propagation that predictions of the Mindlin micromorphic theory may be inefficient if the size of inhomogeneity is comparable with the pulse length. This means that the Mindlin microelasticity is still an approximation of the description of the behavior of materials, which is satisfactory only for long wavelengths or for small size of inhomogeneities.

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References

  1. Berezovski A (2011) Thermodynamic interpretation of finite volume algorithms. J Struct Mech (Rakenteiden Mekaniikka) 44:3–156

    Google Scholar 

  2. Berezovski M, Berezovski A (2012) On the stability of a microstructure model. Comput Mater Sci 52(1):193–196

    Article  MATH  Google Scholar 

  3. Berezovski A, Ván P (2016) Microinertia and internal variables. Contin Mech Thermodyn 28(4):1027–1037

    Article  MathSciNet  MATH  Google Scholar 

  4. Berezovski M, Berezovski A, Engelbrecht J (2010) Numerical simulations of one-dimensional microstructure dynamics. In: AIP conference proceedings, part 1, vol 1233, pp 1052–1057

    Google Scholar 

  5. Berezovski M, Berezovski A, Engelbrecht J (2010) Waves in materials with microstructure: numerical simulation. Proc Estonian Acad Sci 59(2):99–107

    Google Scholar 

  6. Berezovski A, Engelbrecht J, Maugin GA (2008) Numerical simulation of waves and fronts in inhomogeneous solids. World Scientific, Singapore

    Book  MATH  Google Scholar 

  7. Cherkaev A (2004) Approaches to nonconvex variational problems of mechanics. In: Nonlinear homogenization and its applications to composites, polycrystals and smart materials. Springer, Berlin, pp 65–105

    Google Scholar 

  8. Chen Y, Lee JD (2003) Connecting molecular dynamics to micromorphic theory. (I). Instantaneous and averaged mechanical variables. Phys A: Stat Mech Appl 322:359–376

    Google Scholar 

  9. Chen Y, Lee JD (2003) Connecting molecular dynamics to micromorphic theory. (II). Balance laws. Phys A: Stat Mech Appl 322:377–392

    Google Scholar 

  10. Eringen AC, Suhubi ES (1964) Nonlinear theory of simple micro-elastic solids–I. Int J Eng Sci 2(2):189–203

    Article  MathSciNet  MATH  Google Scholar 

  11. Gonella S, Greene MS, Liu WK (2011) Characterization of heterogeneous solids via wave methods in computational microelasticity. J Mech Phys Solids 59(5):959–974

    Article  MATH  Google Scholar 

  12. Green AE, Rivlin RS (1964) Multipolar continuum mechanics. Arch Rationol Mech Anal 17(2):113–147

    MathSciNet  MATH  Google Scholar 

  13. Greene MS, Gonella S, Liu WK (2012) Microelastic wave field signatures and their implications for microstructure identification. Int J Solids Struct 49(22):3148–3157

    Article  Google Scholar 

  14. LeVeque RJ (1997) Wave propagation algorithms for multidimensional hyperbolic systems. J Comput Phys 131(2):327–353

    Article  MATH  Google Scholar 

  15. Maugin GA (2015) Some remarks on generalized continuum mechanics. Math Mech Solids 20(3):280–291

    Article  MathSciNet  MATH  Google Scholar 

  16. Mindlin RD (1964) Micro-structure in linear elasticity. Arch Rationol Mech Anal 16(1):51–78

    MathSciNet  MATH  Google Scholar 

  17. Neff P, Ghiba ID, Madeo A, Placidi L, Rosi G (2014) A unifying perspective: the relaxed linear micromorphic continuum. Contin Mech Thermodyn 26(5):639–681

    Article  MathSciNet  MATH  Google Scholar 

  18. Schröder J, Neff P (2010) Poly-, quasi- and rank-one convexity in applied mechanics, vol 516. CISM courses and lectures. Springer Science & Business Media, Berlin

    Google Scholar 

  19. Voyiadjis GZ, Faghihi D (2014) Overview of enhanced continuum theories for thermal and mechanical responses of the microsystems in the fast-transient process. J Eng Mater Technol 136(4):041,003

    Article  Google Scholar 

  20. Wang X, Lee JD (2010) Micromorphic theory: a gateway to nano world. Int J Smart Nano Mater 1(2):115–135

    Article  Google Scholar 

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Acknowledgements

This chapter is derived in part from the article published in Mech. Res. Commun. (2016) 77:60–64. Copyright\(\copyright \) Elsevier Ltd., available online: http://www.sciencedirect.com/science/article/pii/S0093641316301689

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Correspondence to Arkadi Berezovski .

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Berezovski, A., Ván, P. (2017). One-Dimensional Microelasticity. In: Internal Variables in Thermoelasticity. Solid Mechanics and Its Applications, vol 243. Springer, Cham. https://doi.org/10.1007/978-3-319-56934-5_7

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  • DOI: https://doi.org/10.1007/978-3-319-56934-5_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-56933-8

  • Online ISBN: 978-3-319-56934-5

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