Elasticity and (dis)orders in networks and cellular patterns

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• Dr Marc Durand, Université Paris Diderot
• Friday 19 October 2012, 14:00-15:00
• Oatley Seminar Room, Department of Engineering.

If you have a question about this talk, please contact Ms Helen Gardner.

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Networks are heterogeneous materials whose continuous phase is assembled into slender objects – the links – that are connected to each other at nodes. The macroscopic properties (elasticity, transport,...) of such systems crucially depend on the specific arrangements of their components. In the first part of this talk, I will study the conditions for existence of “optimal networks”, i.e. isotropic networks with highest elastic moduli (and electrical conductivity) for a given density. Using a variational approach in an unconventional way, I will show that a simple set of rules can be established on the geometry and topology of the nodes in such networks. Networks that satisfy these rules can effectively be built and I will provide examples at two and three dimensions. The elastic moduli (and electrical conductivity) of these optimal networks constitute upper-bounds which compete or improve the well-known Hashin-Shtrikman bounds. The second part of the talk will be devoted to the description of disorders in two-dimensional cellular patterns, such as dry foams: the macroscopic properties of these systems are affected by two kinds of disorders: the first one is the geometrical disorder, defined as the relative width of the distribution of cell sizes, and the second one is the topological disorder, defined as the relative width of the distribution of the number of sides of a cell. I will show that in fact these two quantities are strongly correlated: a monodisperse foam contains mostly hexagonal cells, while in a polydisperse foam, larger bubbles have more sides. A model, based on the formalism of statistical mechanics, has been eveloped to explain the quasi-linear dependence of the two disorders.

This talk is part of the Engineering - Mechanics and Materials Seminar Series series.

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