Foams: Models for Elastic, Plastic, Fluid Materials

Thursday, September 30, 2004 - 11:00am - 11:50am
Keller 3-180
Francois Graner (Université de Grenoble I (Joseph Fourier))
It is difficult to predict the constitutive relations of foams, emulsions, granular materials or gels from first principles. Experimentally, the mechanical behaviors of such viscoplastic materials do not appear to change discountinuously. However, mathematical singularities appear as soon as a solid exhibits plastic deformation, or a liquid a non-zero restoring force. The continuum elasticity theory and the Navier-Stokes equations break down.

Visco-elasto-plastic theories require an interpolation between these apparently orthogonal descriptions. We use physical quantities which exist and are measurable in all regimes. We define generalized stress and strain tensors as statistical averages over microscopical details (avoiding the use of a microscopic reference state). They recover each correct limiting behaviors when either classical theory applies.

We perform local and averaged measurements on foam flowing past an obstacle or through a constriction, or under Couette shear. Applications include discrete mechanics, where the sample size (upper cut-off) is not significantly larger than the individual size (lower cut-off): granular materials, nano-fluidics.