BULLETIN of the

POLISH ACADEMY of SCIENCES

TECHNICAL SCIENCES

 BULLETIN of the POLISH ACADEMY of SCIENCES: TECHNICAL SCIENCES
Volume 55, Issue 2, June 2007

Micro and Nano-scale mechanics
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pp 133 - 140

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Nano-mechanics or how to extend continuum mechanics to nano-scale

J. WANG, B.L. KARIHALOO and H.L. DUAN
In a series of recent papers we have shown how the continuum mechanics can be extended to nano-scale by supplementing the equations of elasticity for the bulk material with the generalised Young-Laplace equations of surface elasticity. This review paper begins with the generalised Young-Laplace equations. It then generalises the classical Eshelby formalism to nano-inhomogeneities; the Eshelby tensor now depends on the size of the inhomogeneity and the location of the material point in it. The generalized Eshelby formalism for nano-inhomogeneities is then used to calculate the strain fields in quantum dot (QD) structures. This is followed by generalisation of the micro-mechanical framework for determining the effective elastic properties of heterogeneous solids containing nano-inhomogeneities. It is shown that the elastic constants of nanochannel-array materials with a large surface area can be made to exceed those of the non-porous matrices through pore surface modification or coating. Finally, the scaling laws governing the properties of nano-structured materials are given.
  
Key words: 

surface/interface stress, generalized Young-Laplace equation, Eshelby formalism, effective elastic constants, size
effect, scaling laws
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