Loïc Le Marrec

Université de Rennes 1 | UR1 · Institut de Recherche Mathématique de Rennes - IRMAR

Rayleigh waves measurements are used to characterise cover concrete and mortar in the frequency range 60-180 kHz. At these frequencies, the wavelength is comparable to the size of the aggregates, and waves propagate in a multiple scattering regime. Acquired signals are then difficult to interpret due to an important incoherent part. The method prop...

Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident wavelength is similar to the radius of the inclusions. A purely numerical methodology is presented, with whic...

Riemann–Cartan geometry is used to model continuum with defects. In order to illustrate the dif-ferences induced by two possible definitions for the strain (spatial or material) in this framework, propagation of waves is studied for a simple example of infinite continuum with uniform and stationary defects density. Anisotropy and attenuation are ca...

The present paper proposes analytical formulations of the eigenvalues and eigenfunctions (frequencies and modes) of vibrating rings of any cross-section shape, so as to be applied to engineering problems, like design optimization or life duration improvement. This is done by means of the Timoshenko beam theory accounting for the curved metric throu...

We present an induced geometrically exact theory for the three-dimensional vibration of a beam undergoing finite transformation. The beam model coincides with a curvilinear Cosserat body and may be seen as an extension of the Timoshenko beam model. No particular hypothesis is used for the constitutive laws (in the framework of hyperelasticity), the...

Résumé Je présenterai une initiative citoyenne relative à l’acquisition et au traitement de données libres sur les mobilités. Par mobilité, on entend à la fois le trafic de voitures et poids-lourds mais également les vélos ou piétons (mobilités douces). Cette démarche a été portée par l’association environnementale Agis-Ta-Terre, sur Châteaubourg....

This paper exposes buckling solutions of a plane, quasi-static Timoshenko beam with small transformation subjected to a longitudinal force and surrounded by an elastic wall modeled by two-parameter elastic foundations. A non-dimensional analysis of associated Haringx and Engesser model is performed and buckling stress and shape are exposed analytic...

This paper introduces tools on fibre geometry towards the framework of mechanics of microstructured continuum. The material is modelled by an appropriate bundle for which the associated connection and metric are induced from the Euclidean space by a smooth transformation represented by a fibre morphism from the bundle to Euclidean space. Furthermor...

This paper exposes full analytical solutions of a plane, quasi-static but large transformation of a Timoshenko beam. The problem is first re-formulated in the form of a Cauchy initial value problem where load (force and moment) is prescribed at one end and kinematics (translation, rotation) at the other one. With such formalism, solutions are expli...

Plane bending of a Timoshenko beam is derived using Cosserat formulation by the mean of a material curve and a moving director frame. Equilibrium relations are derived in the case of linear stress-strain relations and for both large strains and large dis-placements. Beam bending is controlled by magnitude and direction of a force and a bending mome...

Bending of a Kirchhoff rod loaded by pure moment is derived using Cosserat formulation by the mean of a material curve and a moving director frame. Equilibrium relations are derived in a dimensionless form. Linear stress-strain relation is adopted with large strain and large displacement. Two invariants dictate the existence of the solutions : the...

Analytical solutions of a plane, quasi-static but large transformation of a Timoshenko beam is exposed. The problem is first re-formulated in the form of a Cauchy initial value problem where load (force and moment) is prescribed at one-end and kinematics (translation, rotation) at another. With such formalism, solutions are explicit for any load. T...

This paper exposes full analytical solutions of a plane, quasi-static but large transformation of a Timoshenko beam. The problem is first re-formulated in the form of a Cauchy initial value problem where load (force and moment) is prescribed at one-end and kinematics (translation, rotation) at the other one. With such formalism solutions are explic...

Analytical solutions of a plane, quasi-static but large transformation of a Timoshenko beam is exposed. The problem is first re-formulated in the form of a Cauchy initial value problem where load (force and moment) is prescribed at one-end and kinematics (translation, rotation) at another. With such formalism, solutions are explicit for any load. T...

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...

Etude comparative des propriétés acoustiques d'une guitare en bois et en carbonne

We are interested in buckling for Timoshenko beam supported along its length by an elastic wall (Winkler foundation) and subjected to a longitudinal force. We use analytical methods to determine buckling load and mode shape rather than numerical methods. Haringx and Engesser models are compared. We show that the rigidity of the wall solely gouverns...

Integrated gas sensors and measuring systems are desired devices in many domains, including large scales applications. One of the main issue still is their poor chemical selectivity despite the very wide diversity of developed systems. In this paper, we present our approach based on selectively adsorbing zeolite thin films. A full instrument has be...

A generalized Timoshenko rod model is developed for helical strands and helically reinforced cylinders. The thermomechanical constitutive law has five effective elastic moduli, and two thermal coefficients, which can be obtained with the finite element method, or partly from analytic solutions. The model predicts nonclassical bending and thermoelas...

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...

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...

A rod model is proposed for simultaneous tension, torsion and bending of helically wound cables. The model is formulated in the Timoshenko beam formalism by first assuming that a cable can be homogenized effectively as a 3D solid rod continuum following Spencer’s constitutive law. The cross-sectional forces and moments are obtained by integrating t...

This study proposes a new enriched finite element method to handle vibrations of rods (traction-compression) and beams (bending) with varying cross-sections.

Elastic wave propagation and scattering in a media containing a continuous density of defect is modeled with a geometrical approach. The material is supposed to be a Riemann–Cartan manifold with a connection enriched by a nonzero torsion. The study is followed until to reveal analytical solutions. The scattering of a defective domain shows explicit...

Riemann-Cartan geometry is used to model continuum with defect. This is performed by introducing an affine (a not simply linear) connection related to the torsion of the manifold. The classical laws of mechanics are then developed according to this new covariant derivative. A new formulation of the Navier equation is obtained under small deformatio...

Poster summarizing my end-of-course internship: Elastomers have specific mechanical properties, particularly their capacity to undergo important distortion on the one hand, and to dissipate energy on the other hand. This is why they are more and more widely used in various industrial fields; especially where materials have to be made leakproof. Thi...

We consider uniform, flat and circular ring where the center of mass G of the cross-section describes a circle in the (O; e x , e y) Cartesian plane and with radius R (Fig.1). Hence, each center of mass is localized by the position vector OG = Re r and curvilinear abscissa S = Rθ in cylindrical basis (e r , e θ , e z). The cross-section is assumed...

Automatic reed valves (suction and discharge) in a reciprocating compressor are noise sources due to free vibrations and structure impacts on limiters and valve seat during a pressure cycle. Understanding the noise source generation and propagation needs a well-modelled pressure cycle in the compressor. Modelling the pressure behaviour in a cylinde...

Riemann-Cartan geometry is used to model continuum with defects. In order to illustrate the differences induced by two possible definitions for the strain (spatial or material) in this framework, propagation of 3D waves is studied for a simple example of infinite continuum with uniform and stationary defects density. Anisotropy and attenuation are...

Riemann-Cartan geometry is used to model continuum with defect. If elastic waves propagate in an infinite continuum with uniform and stationary defects density we observe dispersion, attenuation and anisotropy with a large spectral dependence. Chi-rality and uniform breathing vibrations are observed too. In a second test, defects are concentrated i...

Le diagnostic des structures et l’évaluation de la durée de vie résiduelle des ouvrages est une problématique importante pour le génie civil. Parmi les nombreuses techniques d'auscultation non destructives ultrasonores les ondes de surface sont particulièrement adaptées à la détermination les propriétés mécaniques du béton d'enrobage (les 3 à 5 pre...

Riemann-Cartan geometry is used to model continuum with defects. In order to illustrate the differences induced by two possible definitions for the strain (spatial or material) in this framework, propagation of 3D waves is studied for a simple example of infinite continuum with uniform and stationary defects density. Anisotropy and attenuation are...

Finite difference schemes on regular grids are efficient to accurately predict the seismic wave field, at least for smooth models. However, spurious diffractions become visible when the topography or internal interfaces do not align with the Cartesian grid. We propose to use the generalized finite difference scheme to propagate the wave field on un...

Acoustic multiple scattering is considered. It is shown that the Foldy's assumption can be expanded to a higher order accounting more than one ensemble average. Hypotheses underlying Foldy's assumption and the quasi-crystalline assumption (QCA) are discussed. For a point-like source probing an infinite heterogeneous medium, analytical calculation a...

A new formulation of the effective wave through a heterogeneous medium is the starting point of this paper. The coherent scattered field from a fixed inclusion is supposed to propagate with a complex effective wave number K. The objective is to find the expression of K(ω) according to the concentration of inclusion. This is performed in first order...

The Silences of the Archives, the Reknown of the Story. The Martin Guerre affair has been told many times since Jean de Coras and Guillaume Lesueur published their stories in 1561. It is in many ways a perfect intrigue with uncanny resemblance, persuasive deception and a surprizing end when the two Martin stood face to face, memory to memory, befor...

Multipass welds made in austenitic stainless steel, in the primary circuit of nuclear power plants with pressurized water reactors, are characterized by an anisotropic and heterogeneous structure that disturbs the ultrasonic propagation and challenge the ultrasonic non‐destructive testing. The simulation in this type of structure is now possible th...

The presented study aims at evaluating the bulk elastic Young's modulus of six different concrete mixes as a function of porosity and water content. The impact echo method consists of a frequency analysis of ultrasonic waves generated by the impact of a steel ball. It is commonly used to measure the thickness of large concrete slabs, to detect void...

In the context of structural heritage preservation, monitoring and durability diagnosis by means of non destructive (ND) techniques becomes a more and more important question. In order to establish the empirical and physical relationships between the ND results and the durability indicators of various concretes, an experimental program specially ad...

I gained my PhD in the Laboratory of Mechanics and Acoustics in Marseilles (France). The objective was to define a numerical algorithm able to recover some properties of an immersed body (density, elastic coefficients, size or shape). Experimentally diffraction of ultrasonic pulses was used: measurement was done all around the body and the experi-m...

Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro- or nano-structures. This Note investigates a model of wave propagation in a nonlocal elastic material. We show that a dispersive wave equation is obtained from a nonlocal elastic constitutive law, based on a mixture...

The study presented here aims at evaluating the bulk elastic Young modulus of six different concrete mixes as a function of the water content and degradations due to carbonation or chloride ingress. The frequency analysis of ultrasonic waves in concrete after the impact of a steel ball (impact echo method) is commonly used to measure the thickness...

We are concerned by the design of a non destructive ultrasonic method quantifying porosity of cover concrete. Modification of porosity is a major cause of reinforcing bar corrosion that induces bar swelling and macro-cracks which may cause the ruin of the structure. It is then necessary to characterize the porosity in the first cm above the steel b...

Résumé — Ce travail présente un modèle tri-dimensionnel de poutre tenant compte des glissements transversaux à partir des milieux continus à directeurs de type Cosserat en transformations finies. Le Hessien de la fonctionnelle énergie est calculé dans le formalisme des directeurs permettant l'étude des vibrations autour d'un état pré-contraint. Mot...

Numerous multipass welds in austenitic stainless steel are made on the primary circuits of nuclear power stations. The heterogeneous anisotropic nature of these welds causes disturbance to ultrasonic propagation. Simulation is a useful tool when attempting to understand physical phenomena. With this objective, a finite element code called ATHENA wa...

Numerical simulations are performed to study the propagation of elastic waves in a 2-D random heterogeneous medium such as concrete. To reduce spurious numerical artefacts to a negligible level, a fourth-order time-domain numerical scheme and an immersed interface method are used together. Effective properties of the equivalent homogeneous medium a...

Propagation of elastic waves in heterogeneous medium composed of scatterers embedded in a homogeneous matrix is considered. Both matrix and scatterers are isotropic elastic media. The multiple scattering regime is assumed, and the focus is put on the coherent field obtained by averaging several equivalent realizations of disorder. Classical methods...

This paper deals with the two-dimensional image reconstruction of an elastic tubes using ultrasonic tomographic method based on first-Born approximation and a canonical approximations. The latter improvement makes it possible to extend the scope of tomography from lower impedance contrast media to higher impedance contrast situations, even when the...

It is very common to use pre-stressed beam models in the structure design. However in the nonlinear domain, the modal analysis remains difficult especially when shearability is taken into account. This work aims to study the natural vibrations of pre-stretched nonlinear shearable Timoshenko beam using Cosserat continuum mechanics. In this paper, a...

Numerous multipass welds in austenitic stainless steel are made on the primary circuits of nuclear power stations. The heterogeneous anisotropic nature of these welds causes disturbance to ultrasonic propagation. Simulation is a useful tool when attempting to understand physical phenomena. With this objective, a finite element code called ATHENA wa...

Comparisons were made between the results obtained using two quantitative ultrasound imaging methods on the solid cross section of a cylindrical tube that is infinite in the axial direction. The first method tested was the classical reflection tomography method based on the first-order Born approximation, which can only be used under conditions to...

Des ondes ultrasonores de surface (dans la bande de fréquence 60 kHz – 180 kHz) sont utilisées pour caractériser les premiers centimètres de dalles de bétons. A ces fréquences, la longueur d'onde est du même ordre de grandeur que la dimension des granulats; le caractère fortement hétérogène du béton perturbe la propagation des ondes qui sont alors...

A near-field ultrasonic tomography method providing high resolution imaging for soft tissue in the reflection mode is reported. When the Born approximation is valid, the main limitation of this method is that it requires an incident pulse with infinite bandwidth, whereas the incident pulses used in practice have a limited bandwidth, which makes qua...

The mathematical basis of theories for studying multiple scattering is well understood. However, the real do- main of validity of these methods is still not clearly esablished. This paper presents the frame for a numerical validation of a classical method, the Independent Scattering Approximation, detailing specific implementation and signal proces...

Recent literature has shown great interest for better understanding of the dynamics of slender structures. There are several classical beam models. Among them, the use of Timoshenko model, taking into account the shearability, is known to provide a very good estimation of thick beam dynamics especially for high frequencies. In this study a three di...