Keywords: large scale deformation, open-celled foam, parallel computing.

There is much interest in how materials with complex architectures, such as composites and foams, respond to different loading scenarios in engineering applications. Many of these substances offer advantages over traditional materials such as reduced weight or increased strength. However, the reliable use of composites and foams in engineering applications is not straightforward. One problem is that it is difficult to characterise their bulk properties without taking into account their internal microstructure.

In this paper, the authors further explore the idea of using micro-structural finite element models, based on micro-CT imaging and automatic mesh generation. The motivation is that virtual testing of a micro-structural model can be used to develop a homogenised stress-strain response for later macroscopic analysis. In the case of open celled foams, there are three challenges to deal with in order to facilitate the proposed micro-structural analysis: firstly the solution of complex three dimensional models with millions of unknowns, secondly a capability to represent large strains and thirdly a mechanism to deal with contacts as the foam compacts. In a first step towards solving this type of problem, the authors present work that extends the building block libraries of Smith and Griffiths [1] and of ParaFEM, an open source library for parallel finite element analysis [2]. The new subroutines developed facilitate the modelling of large scale deformations.

Validation of the implementation is carried out using a well known test case that has an analytical solution - the uniaxial strain of a Saint Venant-Kirchoff material. The analyses undertaken using the new parallel program are compared against the analytical solution and FEAP [3], another finite element program. In order to solve very high resolution three dimensional models in a reasonable amount of time, it is essential that the parallel software is scalable over many processors. A study of the parallel performance is undertaken using a 208 core Bull Novascale supercomputer at the University of Manchester. Using 128 processors, the study shows that a 125,000 element problem can be solved in around 30 seconds and a 1,000,000 element problem in around 30 minutes. The authors note that these figures do not represent the limits of the techniques used. Much larger problems can be tackled and much larger numbers of processors can be used.

1

I. M. Smith and D. V. Griffiths. "Programming the Finite Element Method". Wiley, 2004.

2

L. Margetts. ParaFEM webpage. www.parafem.org.uk.

3

R. L. Taylor. "FEAP, A Finite Element Analysis Program. User Manual." December 2000.

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