Rémi Cornaggia

Rémi Cornaggia
Sorbonne Université | UPMC · Institut Jean Le Rond d'Alembert (DALEMBERT)

M.S. Mechanical Eng., Ph. D. Applied maths and Civil Eng. (joint program)

About

17
Publications
1,904
Reads
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59
Citations
Citations since 2017
15 Research Items
59 Citations
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Introduction
I am interested in the modelling and simulation of acoustic and elastic waves, more specifically in inverse scattering problems, vibrations of heterogeneous beams, and homogenisation and optimisation of architected materials. Maths : topological derivatives, integral equations, asymptotic and "mean-fields" homogenisation methods. Numerics : finite elements, boundary elements, FFT-based methods for numerical homogenisation. Full texts : https://cv.archives-ouvertes.fr/remi-cornaggia
Additional affiliations
November 2020 - present
Sorbonne Université
Position
  • Maître de conférences
October 2019 - October 2020
Laboratoire de Mécanique et d’Acoustique
Position
  • PostDoc Position
Description
  • Worked for the company Inovsys as a postdoctoral researcher (part-time at LMA), on the modelling of thermo-visco-elastic composites.
October 2018 - October 2019
Laboratoire de Mécanique et d’Acoustique
Position
  • PostDoc Position
Education
September 2012 - September 2016
University of Minnesota Twin Cities
Field of study
  • Civil Engineering
September 2012 - September 2016
ENSTA ParisTech
Field of study
  • Applied Mathematics
September 2008 - August 2012
Ecole normale supérieure de Cachan
Field of study
  • Mechanical engineering

Publications

Publications (17)
Article
Full-text available
The homogenization of microstructured interfaces requires solving specific problems posed on semi-infinite bands. To tackle these problems with existing FFT-based algorithms, a reformulation of these band problems into fully periodic cell problems, posed on bounded domains, is established. This is performed thanks to a Dirichlet-to-Neumann operator...
Article
This paper presents a procedure for the estimation of the effective thermo-viscoelastic behavior in fiber-reinforced polymer filaments used in high temperature fiber-reinforced additive manufacturing (HT-FRAM). The filament is an amorphous polymer matrix (PEI) reinforced with elastic short glass fibers treated as a single polymer composite (SPC) ho...
Article
Full-text available
An homogenized model is proposed for linear waves in 1D microstructured media. It combines second-order asymptotic homogenization (to account for dispersion) and interface correctors (for transmission from or towards homogeneous media). A new bound on a second-order effective coefficient is proven, ensuring well-posedness of the homogenized model w...
Conference Paper
Full-text available
Aiming to estimate the effective behavior of the parts obtained by fused deposition modeling (FDM) in the case of short fiber composite materials, the Mean-field homogenization procedure, introduced in linear elasticity, is here extended to linear thermo-viscoelasticity. The variation of the parameters describing the state of the fibers inside the...
Article
This works concerns the propagation of waves in periodic media, whose microstructure is optimized to obtain specific dynamical properties (typically, to maximize the dispersion in given directions). The present study, focusing on scalar waves in two dimensions, for example, antiplane shear waves, aims at setting a generic optimization framework. Th...
Article
Full-text available
This work presents a new enriched finite element method dedicated to the vibrations of axially inhomogeneous Timoshenko beams. This method relies on the “half-hat” partition of unity and on an enrichment by solutions of the Timoshenko system corresponding to simple beams with a homogeneous or an exponentially-varying geometry. Moreover, the efficie...
Article
We consider the homogenized boundary and transmission conditions governing the mean-field approximations of 1D waves in finite periodic media within the framework of two-scale analysis. We establish the homogenization ansatz (up to the second order of approximation), for both types of problems, by obtaining the relevant boundary correctors and expo...
Conference Paper
Full-text available
In the context of waves in periodic media , we propose an iterative algorithm that determines an optimal material distribution to reach target effective dispersive properties. It relies on an homogenized model of this medium, an update procedure based on the topological derivative concept, and on an efficient FFT-accelerated method to solve cell pr...
Article
Full-text available
We aim to detect defects or perturbations of periodic media, e.g. due to a defective manufacturing process. To this end, we consider scalar waves in such media through the lens of a second-order macroscopic description, and we compute the sensitivities of the germane effective parameters due to topological perturbations of a microscopic unit cell....
Article
Full-text available
This work presents an enriched finite element method (FEM) dedicated to the numerical resolution of Webster's equation in the time-harmonic regime, which models many physical configurations, e.g. wave propagation in acoustic waveguides or vibration of bars with varying cross-section. Building on the wave-based methods existing in the literature, we...
Article
Full-text available
We consider scalar waves in periodic media through the lens of a second-order effective i.e. macroscopic description, and we aim to compute the sensitivities of the germane effective parameters due to topological perturbations of a microscopic unit cell. Specifically, our analysis focuses on the tensorial coefficients in the governing mean-field eq...
Conference Paper
Full-text available
This study proposes a new enriched finite element method (FEM) to handle high-frequency vibrations of bars (traction-compression) and beams (bending) with varying cross-section. Indeed, analytical solutions are available for a limited number of geometries, especially for Timoshenko beams, and traditional h- and hp-FEM may become costly at increasin...
Article
Full-text available
This article concerns an extension of the topological derivative concept for 3D elasticity problems involving elastic inhomogeneities, whereby an objective function J is expanded in powers of the characteristic size a of a single small inhomogeneity. The O(a 6) approximation of J is derived and justified for an inhomogeneity of given location, shap...
Conference Paper
Full-text available
This study proposes a new enriched finite element method to handle vibrations of rods (traction-compression) and beams (bending) with varying cross-sections.
Conference Paper
Full-text available
We derive the topological derivatives of the homogenized coefficients associated to a periodic material, with respect of the small size of a penetrable inhomogeneity introduced in the unit cell that defines such material. In the context of antiplane elasticity, this work extends existing results to (i) time-harmonic wave equation and (ii) second-or...
Thesis
The purpose of this work was to develop new methods to address inverse problems in elasticity,taking advantage of the presence of a small parameter in the considered problems by means of higher-order asymptoticexpansions.The first part is dedicated to the localization and size identification of a buried inhomogeneity $BTrue$ in a 3Delastic domain....
Conference Paper
Full-text available
In this work, least-squares functionals commonly used for defect identification are expanded in powers of the small radius of a trial inclusion, in the context of time-harmonic elastodynamics, generalizing to higher orders the concept of topological derivative. Such expansion, whose derivation and evaluation are facilitated by using an adjoint stat...

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Projects

Projects (2)
Project
This project aims at exploring the capabilities of coupling (i) the second-order asymptotic (or 'two-scales") homogenization method and (ii) topological derivatives-based methods to study direct and inverse wave problems in periodic materials. In particular, the method captures the anisotropic dispersion effects due to the microstructure, which enables (i) to recover some features of these materials by probing them with long-wavelength waves (i.e. below the classical diffraction limit) and (ii) to build optimization procedures to reach objective dispersive properties.
Project
The objective is to define analyticaly the vibrational behavior of beam with various geometry, material, inital state