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2 2007

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

Wang J., Karihaloo B.L., Duan H.L.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2007

Vol. 55, nr 2

133-140

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 proper-ties 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.

Eshelby formalism for multi-shell nano-inhomogeneities

Yi X., Duan H. L., Karihaloo B. L., Wang J.

Archives of Mechanics

2007

Vol. 59, nr 3

259-281

Nano-particles consisting of a core surrounded by multiple outer shells (multi-shell particles) are used as novel functional materials as well as stiffeners/toughners in conventional composites and nanocomposites. In these heterogeneous particles, the mismatch of thermal expansion coefficients and lattice constants between neighboring shells induces stress/strain fields in the core and shells, which in turn affect the physical/mechanical properties of the particles themselves and/or of the composites containing them. In this paper, we solve the elastostatic inhomogeneous indusion problem of an infinite medium containing a multi-shell spherical particle when the eigenstrains are prescribed in the particle and in the multi-shells, and the inhomogeneity problem when an arbitrary remote stress field is applied to the infinite medium. The corresponding Eshelby and stress concentration tensors of the two problems are obtained and specialised to inhomogeneous inclusions in finite spherical domains with fixed displacement or traction-free boundary conditions. Finally, the Eshelby tensor of a spherical inhomogeneity with non-uniform eigenstrain is obtained and applied to quantum dots of uniform and non-uniform compositions.