Details of Grant 

EPSRC Reference:	GR/S92151/01
Title:	The mathematical theory of homogenization with applications to indusrial & biological composite materials
Principal Investigator:	Parnell, Professor W
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Manchester, The
Scheme:	Postdoc Res Fellowship PreFEC
Starts:	01 October 2004	Ends:	30 September 2007	Value (£):	100,855
EPSRC Research Topic Classifications:	Continuum Mechanics
EPSRC Industrial Sector Classifications:	Manufacturing
Related Grants:
Panel History:	Panel Date Panel Name Outcome 03 Feb 2004 PDF in Mathematics 2003/2004 - Sift Deferred
Summary on Grant Application Form
HOMOGENIZATION IS THE PROCESS OF SMOOTHING OUT QUANTITIES WHICH VARY ON A MICROSTRUCTURAL LENGTHSCALE (LYING BETWEEN THE ATOMIC AND MACROSCOPIC SCALES) IN ORDER TO OBTAIN SOME EFFECTIVE MACROSCOPIC PROPERTY. THE AIM OF THE PROPOSED RESEARCH IS TO DEVELOP THE CURRENT MATHEMATICAL THEORY IN ORDER TO UNDERSTAND AND PREDICT THE DEPENDENCE OF EFFECTIVE MATERIAL PROPERTIES ON MORE COMPLICATED MICROSTRUCTURAL PHENOMENA THAN PREVIOUSLY ADDRESSED. THE THEORY WILL BE APPLIED TO TWO AREAS WHERE HOMOGENIZATION PROCESSES OCCUR FREQUENTLY. THE FIRST IS THE MODELLING OF INDUSTRIAL COMPOSITE MATERIALS AND IN PARTICULAR TO VISCOELASTIC MEDIA USED ON THE EXTERNAL WALLS OF UNDERWATER VEHICLES. THIS ASPECT OF THE RESEARCH WILL BE A COLLABORATION WITH THE DEFENCE SCIENCE AND TECHNOLOGY LABORATORIES (DSTL) AND THALES UNDERWATER SYSTEMS (TUS). THE SECOND APPLICATION IS TO BIOLOGICAL STRUCTURES WHERE THERE EXIST NATURAL MICROSTRUCTURES, FOR EXAMPLE THE POROUS, CELLULAR NATURE OF BONE AND THE ALVEOLI IN THE LUNGS. MUCH OF THE RESEARCH UNDERTAKEN INTO THE EFFECTIVE RESPONSE OF THESE STRUCTURES HAS THUS FAR PRIMARILY BEEN CONDUCTED EITHER EXPERIMENTALLY OR COMPUTATIONALLY AND SO ANALYTICAL WORK USING HOMOGENIZATION TECHNIQUES WOULD BE OF FUNDAMENTAL INTEREST AS WELL AS OFFERING THE POTENTIAL FOR USEFUL PREDICTIVE MODELS.
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Organisation Website:	http://www.man.ac.uk