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SUMMARY:Acoustic and elastic wave propagation in microstructured media wit
 h interfaces: homogenization\, simulation and optimization - Marie Touboul
  (University of Manchester)
DTSTART:20220509T140000Z
DTEND:20220509T150000Z
UID:TALK174212@talks.cam.ac.uk
CONTACT:Alistair Hales
DESCRIPTION:In this presentation\, the focus is on wave propagation in per
 iodic microstructured media in the presence of interfaces. The dynamic hom
 ogenization of these media and the design of the microstructures to achiev
 e a given macroscopic effect are studied. In a first part\, homogenization
  and optimization are carried out for thin microstructured layers. In a se
 cond part\, the homogenization of periodic microstructures in all spatial 
 dimensions is addressed. \nThe first part concerns the case where the hete
 rogeneities constitute a periodic row of inclusions immersed in a homogene
 ous matrix. When the physical parameters of the inclusions are strongly co
 ntrasted with those of the matrix\, internal resonances can occur and be u
 sed to maximise acoustic absorption. The homogenization of such a resonant
  microstructured layer is studied using a method of matched asymptotic exp
 ansions and leads to non-local jump conditions. The introduction of auxili
 ary variables allows to get a local evolution problem in time which is the
 n solved numerically by an ADER scheme coupled with an immersed interface 
 method. This methodology is validated (local truncation error analysis\, c
 omparison with analytical solutions) and makes possible wave diffraction s
 imulations by resonant meta-interfaces. Finally\, the sensitivity of the e
 ffective parameters to the geometry of the microstructure is determined us
 ing topological derivatives. We then implement a topological optimization 
 procedure for the design of non-resonant thin microstructured layers. \nOn
  the other hand\, it is often assumed that the contact between the inclusi
 ons and the homogeneous matrix is perfect. Some models\, such as spring-ma
 ss conditions\, account for the behaviour of imperfect contacts between so
 lids. In the second part of the thesis\, low-frequency volume homogenizati
 on of such configurations is carried out to obtain the expression of the h
 omogenized fields at order 1\, and an extension to non-linear contacts is 
 presented. Finally\, dispersion diagrams in 1D solids with spring-mass con
 ditions are studied. The framework of high-frequency homogenization is use
 d and an approximation of the fields to the leading order\, as well as dis
 persion relations near the edges of the Brillouin zone is obtained\n
LOCATION:MR20
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