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SUMMARY:Intro talk: Emergence of Willis constitutive coupling in elastodyn
 amic heterogeneous media - William Parnell (University of Manchester)
DTSTART:20230321T090000Z
DTEND:20230321T100000Z
UID:TALK195607@talks.cam.ac.uk
DESCRIPTION:\n\n\nCo-authors - Philip A Cotterill\, David Nigro\, Marie To
 uboul\n\n\n\n\nAbstract:\nWe will begin this talk with an introduction to 
 the formalism of scattering and multiple scattering in linear elastic medi
 a. We work entirely in two dimensions\, describing scattering by a circula
 r\, traction-free void in an isotropic elastic medium and subsequently sho
 w that as the medium becomes highly incompressible (e.g. rubber-like)\, a 
 low-frequency resonance arises\; the Giant Monopole Resonance (GMR). This 
 can be allied with the &ldquo\;rigid-in-soft&rdquo\; (RSR) resonance that 
 has been employed in metamaterials science since the early 2000s\, for the
  basis of numerous acoustic and elastodynamic metamaterials.\nWe employ th
 e multiple scattering formalism to illustrate how the resonators described
  above behave when they are in close proximity\, so that multiple scatteri
 ng effects cannot be neglected. We associate the terms &ldquo\;co-void&rdq
 uo\; and &ldquo\;co-dipole&rdquo\; resonators with pairs of such scatterer
 s in the case of the GMR and RSR respectively. We make the following concl
 usions:\n1.&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\; Co-void resonators a
 llow a lower frequency resonance compared to a single GMR of the same cros
 s-sectional area\, but the resonant strength is largely unaffected.\n2.&nb
 sp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\; Co-dipole resonators allow a much 
 stronger resonance than an isolated RSR\, but the resonant frequency is la
 rgely unaffected.\nThese resonators are thus suggested as the basis for fu
 ture elastodynamic metamaterials.\nFollowing this we move onto the conside
 ration of dynamic constitutive coupling associated with heterogeneous/inho
 mogeneous elastic materials. It is now well established that a general and
  inclusive dynamic constitutive law in acoustics and elasticity is that wh
 ich involves Willis coupling\, embedded in the Milton-Brianne-Willis equat
 ions. Its analogue in electrodynamics is bianisotropy. We will describe th
 e emergence of this coupling phenomena from the starting point of the form
 -invariance of the governing equations to spatial transformations\, and fr
 om material symmetry.\nFinally\, we link the first two parts of the talk w
 ith an example of an inhomogeneous slab consisting of arrays of GMRs embed
 ded in an elastic medium. We present results for the case of normal incide
 nce where Willis coupling is required for the concept of dynamic homogeniz
 ation to be valid. Of specific interest is the case where we allow the sla
 b medium to be lossy and where we employ asymmetry in the arrays. This lea
 ds to reciprocal\, direction-dependent absorption.\nWe close with discussi
 on of oblique incidence\, with specific reference to which components of t
 he coupling tensor can be discerned from reflection and transmission coeff
 icients.\n\n\n\n\n\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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