Inhomogeneous media: constitutive modelling, configurable metamaterials and hyperelastic cloaks
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Inhomogeneous media: constitutive modelling, configurable metamaterials and hyperelastic cloaks
Wed, 21/10/2015 - 14:15 to 15:15
Location:
Speaker:
Dr William J. Parnell
Affiliation:
University of Manchester
Synopsis:
Inhomogeneous media are ubiquitous in science and engineering and also arise frequently in natural contexts. Composites, smart materials and metamaterials are examples of synthetic media, designed in order to optimize specific properties or to give rise to properties that are beyond the realm of naturally occurring media. In this talk an overview will be given of some of the work currently being undertaken in the area of inhomogeneous media within the “Waves in Complex Continua” research group within the School of Mathematics at Manchester.
Initial discussion will focus on the modelling of two materials exhibiting complex nonlinear response - syntactic foams, used in a variety of applications in industry and tendon. The common link is how to upscale the microstructural response into an overall or effective macroscopic response. In the case of tendon the behaviour is strongly nonlinear and hysteretic, arising from a viscoelastic response.
This discussion will then be followed by considering wave propagation problems – specifically those associated with tuneable or “configurable” metamaterials and hyperelastic cloaks. In both cases nonlinear elastic pre-stress is used to modify the response of the medium in question to wave propagation. In the first case it permits band-gaps (frequency ranges of forbidden propagation) to be shifted, annihilated or induced and the second it permits waves to be guided around specific regions of space so as to cloak that area from vibration. The notion of active cloaking will also be considered.
Biography:
Dr William J. Parnell is a Reader in Applied Mathematics and currently holds an EPSRC Research Fellowship. In 1999 he graduated with a first class honours degree in Mathematics from the University of Bristol before moving to the University of Oxford where he obtained a distinction in the MSc in Mathematical Modelling in 2000. His PhD, obtained in 2004 from the University of Manchester, focused on the Mathematical modelling of complex materials and was sponsored by industry. He then held research fellowship positions until 2009 when he was appointed Lecturer in Applied Mathematics at Manchester, before being promoted to Senior Lecturer in 2011 and Reader in 2012. He is interested in the development of novel applied mathematics and enjoys sitting at the interface of mathematics with other fields including engineering, physics, materials science and biomechanics. He mainly works on problems associated with wave phenomena (acoustics and elastic waves) in complex materials as well as the development of mathematical models of the behaviour of such media and has published extensively in these areas. He believes strongly in the engagement of Applied Mathematics with other disciplines and with industry. As Programme Director of the MSc in Applied Mathematics at Manchester he has developed strong links with a broad range of companies in order to provide future opportunities for students. Together with Prof I. David Abrahams he leads the “Waves in Complex Continua” research group at Manchester and has supervised 6 PhD students to completion.