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H/F Thesis proposal : Implementation of cloaking behavior on plate by programmable metamaterials

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Date Limite Candidature : jeudi 26 mai 2022

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General information

Reference : UMR5513-MANCOL-001
Workplace : ECULLY
Date of publication : Thursday, May 5, 2022
Scientific Responsible name : Manuel Collet
Type of Contract : PhD Student contract / Thesis offer
Contract Period : 36 months
Start date of the thesis : 5 September 2022
Proportion of work : Full time
Remuneration : 2 135,00 € gross monthly

Description of the thesis topic

Realization of wave cloaking in plate is complex and necessitates different approximations. Active cloak approach uses a set of discrete multipole sources distributed in space. When the source positions and amplitudes are carefully specified the active field destructively interferes with an incident time harmonic wave so as to nullify the total field in some finite domain and ensure that in the far field only the incident wave is present i.e. the active field is non-radiating. The methodology needs displacement field measurement in the whole domain and can only be implemented for harmonic responses. Another way consists in building appropriate lattice presenting effective spatial distribution of mass and stiffness coefficients for approximating theoretical cloaking equation. In most of the papers [addressing the design of cloaks for linear waves, a singular radially symmetric push-out spatial transformation is employed which maps a point to a finite disc. Such approaches can give good results for theoretical and computational models of continuous media but introduce strong difficulties for practical implementations. In particular, not only does the transformation lead to infinite wave speeds on the interior boundary of the cloak, but also the required cloaking material is characterized by an unrealistic strong anisotropy in stiffness but also on inertial terms that become tensorial terms. A lattice structure, instead of a continuum, can be used for creating approximation of an invisibility cloak. A significant advantage of lattices is that they naturally accommodate high contrasts in their compliance leading to strong anisotropy. However, a radial discrete cloak that fits inside a circular ring would not match any periodic lattice, and the presence of a geometrical mis-match on the interface boundary leads to a substantial mis-match in the interface boundary conditions. The following way used in this project would be to adjust cloaking band embedded into a square lattice which would be subjected to out-of-plane flexural vibration.
As previously demonstrated in different works, one can adjust effective bending stiffness of a piezoelectric composite plate cell by adjusting shunting circuit. Different applications have been made for multimodal stabilization, waves reflection or lensing in plate. The numerical programming of the synthetized electrical shunts paves the way of implementing gradient and/or adaptive function outperforming the standard serial resistance and inductance, or negative capacitance. Based on this capability in programming effective electromechanical behavior this thesis aims at studying implementation of a gradient of controlling shunt function able to produce necessary variation of effective mass density and stiffness for synthetizing approximation of cloaking behavior as proposed by .
The thesis will address the design of this innovative system in two scale level for continuous and discrete implementation. It can be decomposed into :
1. Design and optimization of continuous gradient behavior allowing to establish a square cloak zone in a large frequency band for an infinite plate. The output of this subtask will be the square dimension and the targeted frequency band.
2. Based on the effective mass and stiffness coefficient the second step will focus on the design of local unit piezoelectric cells able to produce this specific behavior using a suitable shunting function. The designing cell and the specified control strategy will be used by other partners for processing and testing.
3. Back to mesoscale, different modelling approaches will be furnished for the finite plate modeling incorporating different uncertainties. Specific homogenization approaches will developed as relaxed micromorphic model or KUBG law frequency band model guaranteeing the link to the control strategy parameters. This model will be used by project partners for developing decision support tools for the robust design and optimization of the adaptive meta-composites.
4. The produced tools and improved models will be made in an iterative process accounting feedback loop between computing and testing for improving cells electromechanical design, programming constraint and parameters sensitivity. Such interaction is a part of the delivery aiming at developing computation/experimental simulation. The last expectation of this part is also the parameter calibration.

Work Context

Adaptive materials are materials with additional properties compared to classical materials (sensing or actuation in this project because of the use of piezoelectric materials). They can thus act directly on their environment and improve the global properties of the structure in which they are integrated (durability, efficiency, instantaneous response to environment stimuli). Composites, on the other hand, are key materials for many fields (transport, aeronautics, renewable energies, etc.). They meet the need to lighten parts while maintaining excellent mechanical properties. The combination of these two technologies allows the emergence of "super" materials with controllable structural properties: adaptive meta-composites. They possess new custom properties, developed according to a functional specification.
The technological challenges associated with these materials and their use in structures are well identified and have the potential to address major societal challenges and Sustainable Development Goals of the 2030 Agenda adopted at the United Nations. These challenges concern, on the one hand, the increase of the durability of composite structures and, on the other hand, their robust design methodologies. The ASTRIA project aims at paving the way toward decision support tools to master the robust design of complex controllable, multiphysical and multiscale structures such as adaptive meta-composite structures based on piezoelectric materials. The chosen example concerns the implementation of cloaking behavior on a continuous plate by programmable metamaterials.

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