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Spatial and Temporal Scaling Affected by System Inhomogeneity: Atomic, Microscopic and Macroscopic

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Abstract

The impetus of nanotechnology has shed light on the direction of new research for many fields and continuum mechanics is no exception. The current trend is to reach down the scale such that all disciplines would meet and benefit from one another. However, there are overwhelming difficulties associated with the discontinuities of results from the various scales. The prevailing gaps in materials and continuum theories are being referred to “Mesomechanics” [1]. Mesoelectronics has in fact discovered that the heat transfer behavior of small bodies is dinstinctly different and requires fundamental studies of electronics at the subatomic scale. New physical laws may have to be discovered to fill in the gaps. The final answer lies in multiscaling [2,3] where the results at the smaller scales must be translated to the macroscopic level.

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  • DOI: 10.1007/1-4020-4972-2_15
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References

  1. Prospects of Mesomechanics in the 21st Century: Current Thinking on Treatment of Multiscale Mechanics Problems, in: G. C. Sih and V. E. Panin, J. of Theoretical and Applied Fracture Mechanics, 37(1–3)(2001) 1–410.

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  2. G. C. Sih and X. S. Tang, Dual scaling damage model associated with weak singularity for macroscopic crack possessing a micro/mesoscopic notch tip, J. of Theoretical and Applied Fracture Mechanics, 42(1) (2004) 1–24.

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  3. G. C. Sih and X. S. Tang, Simultaneity of multiscaling for macro-meso-micro damage model represented by strong singularities, J. of Theoretical and Applied Fracture Mechanics, 42(3) (2004) 199–225.

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  4. G. C. Sih, Thermomechanics of solids: nonequilibrium and irreversibility, J. of Theoretical and Applied Fracture Mechanics, 9(3) (1988) 175–198.

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  5. G. C. Sih, Some basic problems in nonequilibrium thermomechanics, in: S. Sienietyez and P. Salamon, (eds.), Flow, Diffusion and Rate Processes, Taylor and Francis, New York, (1992) 218–247.

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  6. G. C. Sih and X. S. Tang, Singularity representation of multiscale damage due to inhomogeneity with mesomechanics consideration, G. C. Sih, T. Kermanidis and Sp. Pantelakis, eds., Sarantidis Publications, Patras, Greece (2004) 1–15.

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© 2006 Springer

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Sih, G.C. (2006). Spatial and Temporal Scaling Affected by System Inhomogeneity: Atomic, Microscopic and Macroscopic. In: Gdoutos, E.E. (eds) Fracture of Nano and Engineering Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4972-2_15

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  • DOI: https://doi.org/10.1007/1-4020-4972-2_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-4971-2

  • Online ISBN: 978-1-4020-4972-9

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