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University of Cambridge > Talks.cam > Engineering Department Bio- and Micromechanics Seminars > Theory of Elasticity at the Nanoscale

## Theory of Elasticity at the NanoscaleAdd to your list(s) Download to your calendar using vCal - Professor Bhushan Karihaloo, Cardiff University
- Friday 13 November 2009, 14:00-15:00
- Oatley Seminar Room, Department of Engineering.
If you have a question about this talk, please contact Ms Helen Gardner. We have shown in a series of recent papers that the classical theory of elasticity can be extended to the nanoscale by supplementing the equations of elasticity for the bulk material with the generalized Youngâ€“Laplace equations of surface elasticity in order to capture the often unusual mechanical and physical properties of nano-structured particulate and porous materials. This talk, based on the review paper Advances in Applied Mechanics (42, 2009, 1-68), will describe how this has been done. It will begin with a description of the generalized Youngâ€“Laplace equations. It will then generalize 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. Then the stress concentration factor of a spherical nanovoid is calculated, as well as the strain fields in quantum dots (QDs) with multi-shell structures and in alloyed QDs induced by the mismatch in the lattice constants of the atomic species. This will be followed by a generalization of the micromechanical framework for determining the effective elastic properties and effective coefficients of thermal expansion of heterogeneous solids containing nano-inhomogeneities. It will be shown, for example, that the elastic constants of nanochannel-array materials with a large surface area can be made to exceed those of the nonporous matrices through pore surface modification or coating. Finally, the scaling laws governing the properties of nano-structured materials are derived. The underlying cause of the size dependence of these properties at the nanoscale is the competition between surface and bulk energies. These laws provide a yardstick for checking the accuracy of experimentally measured or numerically computed properties of nano-structured materials over a broad size range and can thus help replace repeated and exhaustive testing by one or a few tests. This talk is part of the Engineering Department Bio- and Micromechanics Seminars series. ## This talk is included in these lists:- All Talks (aka the CURE list)
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