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.

}, type={ArtykuĹ‚y / Articles}, title={Nano-mechanics or how to extend continuum mechanics to nano-scale}, volume={vol. 55}, number={No 2}, pages={133-140}, journal={Bulletin of the Polish Academy of Sciences: Technical Sciences}, keywords={surface/interface stress, generalized Young-Laplace equation, Eshelby formalism, effective elastic constants, size effect, scaling laws}, }