MetaMAT’s 7th webinar S2 - 16.11.2021 - Q&A - Marie Touboul
Seminar 7 S2, Tuesday 16th November 2021, 14:00 (London Time)
Title: Acoustic and elastic wave propagation in microstructured media with interfaces: homogenization, simulation and optimization
Speaker: Marie Touboul (Department of Mathematics, University of Manchester, UK)
Abstract: The design of media at a microstructured scale allows to control wave propagation in a fine way and to obtain exotic effects at the macroscopic scale. Thanks to homogenization methods, the microstructure can be advantageously replaced, at the macro scale, by a homogeneous effective medium. Then, it raises the question of optimization tools in order to design the microstructure that allows to achieve a desired macroscopic effect. In this context, the consideration of interfaces (microstructured interfaces, imperfect interfaces) can lead to modifications in the homogenization methods, the numerical methods, or the optimization methods classically used. Two different cases of interfaces will be presented (PhD work, supervised by Cédric Bellis and Bruno Lombard):
(i) Homogenization and optimization are first carried out for microstructured interfaces. The homogenization of a highly contrasted, and therefore resonant, microstructured interface is studied in the time-domain and leads to resonant jump conditions on an effective interface (coll: Kim Pham, Agnès Maurel, Jean-Jacques Marigo). The introduction of auxiliary variables allows to get a local evolution problem in time which is then solved numerically to perform time-domain simulations for the effective resonant meta-interface. Finally, the sensitivity of the effective non-resonant model to the geometry of the microstructure is determined using topological derivatives (coll: Rémi Cornaggia) in order to develop a topological optimization of the microstructure.
(ii) Homogenization of solids with imperfect interfaces of the spring-mass type is then performed (coll: Raphaël Assier). The wavefields are approximated at low-frequency for possibly nonlinear cracks. An approximation of both the wavefields and the dispersion relation is also obtained at higher frequencies for a 1D array of linear cracks.
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Title: Acoustic and elastic wave propagation in microstructured media with interfaces: homogenization, simulation and optimization
Speaker: Marie Touboul (Department of Mathematics, University of Manchester, UK)
Abstract: The design of media at a microstructured scale allows to control wave propagation in a fine way and to obtain exotic effects at the macroscopic scale. Thanks to homogenization methods, the microstructure can be advantageously replaced, at the macro scale, by a homogeneous effective medium. Then, it raises the question of optimization tools in order to design the microstructure that allows to achieve a desired macroscopic effect. In this context, the consideration of interfaces (microstructured interfaces, imperfect interfaces) can lead to modifications in the homogenization methods, the numerical methods, or the optimization methods classically used. Two different cases of interfaces will be presented (PhD work, supervised by Cédric Bellis and Bruno Lombard):
(i) Homogenization and optimization are first carried out for microstructured interfaces. The homogenization of a highly contrasted, and therefore resonant, microstructured interface is studied in the time-domain and leads to resonant jump conditions on an effective interface (coll: Kim Pham, Agnès Maurel, Jean-Jacques Marigo). The introduction of auxiliary variables allows to get a local evolution problem in time which is then solved numerically to perform time-domain simulations for the effective resonant meta-interface. Finally, the sensitivity of the effective non-resonant model to the geometry of the microstructure is determined using topological derivatives (coll: Rémi Cornaggia) in order to develop a topological optimization of the microstructure.
(ii) Homogenization of solids with imperfect interfaces of the spring-mass type is then performed (coll: Raphaël Assier). The wavefields are approximated at low-frequency for possibly nonlinear cracks. An approximation of both the wavefields and the dispersion relation is also obtained at higher frequencies for a 1D array of linear cracks.
Follow us on: www.meta-mat.org
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