Engineering Mechanics Institute Conference 2015

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From local structural characterisation of porous materials to structure-property relations: a systematic approach

Porous and cellular materials are taking an increasingly key role in modern technology due to a combination of unique properties: solid-like mechanics, low density, large surface to bulk ratio and permeability to flow. A key to performance in most applications, as well as to understand their failure, is the pore-scale structure.
I describe a several-stage systematic method to characterise the local structure quantitatively and upscale this description, using a statistical mechanical approach, to derive relations between the pore-scale structural characteristics and large-scale properties / behaviour.

The first stage involves a quantitative description of the local structure, based on a tensorial description of basic volume elements, called quadrons. This in itself is progress in that large-scale behaviour can be related quantitatively to small-scale characteristics.

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.

The third stage, the structural expectation values are used to derive the expectation distribution of local physical properties, such as the permeability to fluid, heat exchange and reactive transport.

In the fourth stage, the physical features are used to construct numerically large equivalent networks, making possible prediction of large-scale measurable properties.

Further homogenisation and coarse-graining to the continuum is then possible by using conventional methods, e.g. effective-medium.

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

1. R. Blumenfeld, S.F. Edwards, Phys.Rev.Lett. 90, 114303 (2003);
2. R. Blumenfeld, S.F. Edwards, Eur.Phys.J. E 19, 23 (2006).
3. R. Blumenfeld, J. Jordan, S.F. Edwards, Phys.Rev.Lett. 109, 238001 (2012)

* Also at:
1. Earth Science and Engineering, Imperial College London, UK
2. Cavendish Laboratory, Cambridge, UK


Raphael Blumenfeld    
National University of Defence Technology and Imperial College London


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