# FMS

## Seminar

### Characterisation and statistical mechanics of disordered foam structures

Seminar Room 1, Newton Institute

#### Abstract

Co-authors: Joseph F. Jordan (Imperial College London), Rebecca Hihinashvili (Imperial College London)The pore-scale structure of foams and cellular (open or closed) materials impacts significantly their large-scale transport and mechanical properties. A systematic several-stage method is described to derive relations between cell-scale structural characteristics and macro-scale properties in two- and three-dimensions.

The first stage involves a quantitative description of the local structure, using a tensor that captures the features most relevant to a number of physical mechanisms. The locality of the tensorial description is achieved by specialized volume elements, called quadrons. Advantages over traditional Voronoi-based descriptions are pointed out.

In the second stage, the description is used in an entropy-based statistical mechanical formalism, making possible the derivation of global structural properties as expectation values over a certain partition function.

In the third stage, we propose to use relations between structural and physical properties (e.g. permeability and heat transfer in solidified open cell foams) in order to translate the structural expectation values into expected distribution of local constitutive properties of equivalent networks.

In the fourth stage the network properties are computed on the scale of a large number of nodes, allowing us to predict upscaled properties at this scale. Further homogenisation and coarse-graining to the continuum is then possible, using conventional methods, such as effective-medium method.

The development of this programme is ongoing and initial tests of some aspects of it are presented in two- and three-dimensional systems.

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