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.

JO - Bulletin of the Polish Academy of Sciences: Technical Sciences L1 - http://sd.czasopisma.pan.pl/Content/111479/PDF/%2855-2%29133.pdf L2 - http://sd.czasopisma.pan.pl/Content/111479 PY - 2007 IS - No 2 EP - 140 KW - surface/interface stress KW - generalized Young-Laplace equation KW - Eshelby formalism KW - effective elastic constants KW - size effect KW - scaling laws A1 - Wang, J. A1 - Karihaloo, B.L. A1 - Duan, H.L. VL - vol. 55 JF - Bulletin of the Polish Academy of Sciences: Technical Sciences SP - 133 T1 - Nano-mechanics or how to extend continuum mechanics to nano-scale DA - 2007 UR - http://sd.czasopisma.pan.pl/dlibra/docmetadata?id=111479 ER -