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Abstract

Small structures formed from a countable number of particles (atoms or molecules) and whose physical and chemical properties are functions of their sizes, are called nanoscopic structures. These structures are located between individual atoms (the size of an atom being about 0.1 nm) and large clusters consisting of up to \(10^8\) atoms or molecules.

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References

  1. A. Satoh, Introduction to Practice of Molecular Simulation (Elsevier, London, 2011)

    Google Scholar 

  2. W.K. Liu, E.G. Karpov, S. Zhang, H.S. Park, An introduction to computational nanomechanics and materials. Comput. Methods Appl. Mech. Eng. 193, 1529–1578 (2004)

    Article  MathSciNet  Google Scholar 

  3. H. Weiss, P. Deglmann, P.J. in’t Veld, M. Cetinkaya, E. Schreiner, Multiscale materials modeling in an industrial environment, Ann. Rev. Chem. Biomol. 7, 65–86 (2016)

    Article  Google Scholar 

  4. N. Ramakrishnan, P.B. Sunil Kumar, R. Radhakrishnan, Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins. Phys. Rep. 543, 1–60 (2014)

    Article  MathSciNet  Google Scholar 

  5. T.S. Gates, G.M. Odegard, S.J.V. Frankland, T.C. Clancy, Computational materials: multi-scale modeling and simulation of nanostructured materials. Compos. Sci. Technol. 65, 2416–2434 (2005)

    Article  Google Scholar 

  6. R.E. Rudd, J.Q. Broughtony, Coarse grained molecular dynamics and the atomic limit of finite elements. Phys. Rev. B 58, R5893–R5896 (1998)

    Article  Google Scholar 

  7. J. Fatemi, F. Vankeulen, P.R. Onck, Generalized continuum theories: application to stress analysis in bone. Meccanica 37, 385–396 (2002)

    Article  MathSciNet  Google Scholar 

  8. H. Rafii-Tabar, E. Ghavanloo, S.A. Fazelzadeh, Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures. Phys. Rep. 638, 1–97 (2016)

    Article  MathSciNet  Google Scholar 

  9. Y. Yoshiyuki, An intrinsic theory of a Cosserat continuum. Int. J. Solids Struct. 4, 1013–1023 (1968)

    Article  Google Scholar 

  10. A.C. Eringen, E.S. Suhubi, Nonlinear theory of simple micro-elastic solidsI. Int. J. Eng. Sci. 2, 189–203 (1964)

    Article  Google Scholar 

  11. A.R. Hadjesfandiari, G.F. Dargush, Couple stress theory for solids. Int. J. Solids Struct. 48, 2496–2510 (2011)

    Article  Google Scholar 

  12. R.D. Mindlin, N.N. Eshel, On first strain-gradient theories in linear elasticity. Int. J. Solids Struct. 4, 109–124 (1968)

    Article  Google Scholar 

  13. H. Askes, E.C. Aifantis, Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results. Int. J. Solids Struct. 48, 1962–1990 (2011)

    Article  Google Scholar 

  14. C.W. Lim, G. Zhang, J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids 78, 298–313 (2015)

    Article  MathSciNet  Google Scholar 

  15. A.C. Eringen, Nonlocal Continuum Field Theories (Springer, NewYork, 2002)

    MATH  Google Scholar 

  16. V.B. Shenoy, R. Miller, E.B. Tadmor, D. Rodney, R. Phillips, M. Ortiz, An adaptive finite element approach to atomic-scale mechanics-the quasi continuum method. J. Mech. Phys. Solids 47, 611–642 (1999)

    Article  MathSciNet  Google Scholar 

  17. A.C. Eringen, Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10, 425–435 (1972)

    Article  Google Scholar 

  18. A.C. Eringen, D.G.B. Edelen, On nonlocal elasticity. Int. J. Eng. Sci. 10, 233–248 (1972)

    Article  MathSciNet  Google Scholar 

  19. A.C. Eringen, C.G. Speziale, B.S. Kim, Crack-tip problem in non-local elasticity. J. Mech. Phys. Solids 25, 339–355 (1977)

    Article  MathSciNet  Google Scholar 

  20. D. Rogula, Nonlocal Theory of Material Media (Springer, Berlin, 1982)

    Book  Google Scholar 

  21. S. Gopalakrishnan, S. Narendar, Wave Propagation in Nanostructures: Nonlocal Continuum Mechanics Formulations (Springer, Switzerland, 2013)

    Book  Google Scholar 

  22. D. Karlicic, T. Murmu, S. Adhikari, M. McCarthy, Nonlocal Structural Mechanics (Wiley-ISTE, London, 2016)

    MATH  Google Scholar 

Download references

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Ghavanloo, E., Rafii-Tabar, H., Fazelzadeh, S.A. (2019). Introduction. In: Computational Continuum Mechanics of Nanoscopic Structures. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-11650-7_1

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  • DOI: https://doi.org/10.1007/978-3-030-11650-7_1

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