Publications

2022

• DAMPING OPTIMIZATION OF VISCOELASTIC CANTILEVER BEAMS AND PLATES UNDER FREE VIBRATION
  
  • Joubert A
  • Allaire G
  • Amstutz S
  • Diani J
  Computers & Structures, Elsevier, 2022. The goal of this work is to significantly enhance the damping of linear viscoelastic structures under free vibration by relying on optimal design. Homogeneous cantilever slender beams and plates satisfying, respectively, the Euler-Bernoulli and Kirchhoff-Love assumptions are considered. A sizing optimization of the beam or plate thickness is proposed, as well as a coupled optimization of the thickness and geometry of the plate applying Hadamard's boundary variation method. The isotropic linear viscoelastic material is modeled by a classical generalized Maxwell model, well suited for polymers. Gradients of the objective functions are computed by an adjoint approach. Optimization is performed by a projected gradient algorithm and the mechanical models are evaluated by the finite element method. Numerical tests indicate that the optimal designs, as well as their damping properties, strongly depend on the material parameters.
• Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors
  
  • Mcmahan Connor
  • Akerson Andrew
  • Celli Paolo
  • Audoly Basile
  • Daraio Chiara
  Journal of the Mechanics and Physics of Solids, Elsevier, 2022, 166, pp.104934. In this work, we construct an effective continuum model for architected sheets that are composed of bulky tiles connected by slender elastic joints. Due to their mesostructure, these sheets feature quasi-mechanisms-low-energy local kinematic modes that are strongly favored over other deformations. In sheets with non-uniform mesostructure, kinematic incompatibilities arise between neighboring regions, causing out-of-plane buckling. The effective continuum model is based on a geometric analysis of the sheets' unit cells and their energetically favorable modes of deformation. Its major feature is the construction of a strain energy that penalizes deviations from these preferred modes of deformation. The effect of non-periodicity is entirely described through the use of spatially varying geometric parameters in the model. Our simulations capture the out-of-plane buckling that occurs in non-periodic specimens and show good agreement with experiments. While we only consider one class of quasi-mechanisms, our modeling approach could be applied to a diverse set of shape-morphing systems that are of interest to the mechanics community. (10.1016/j.jmps.2022.104934)
  DOI : 10.1016/j.jmps.2022.104934
• Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials
  
  • Barré Mathieu
  • Grandmont Céline
  • Moireau Philippe
  Evolution Equations and Control Theory, American Institute of Mathematical Sciences (AIMS), 2022, 12 (3), pp.846-906. In this paper, we thoroughly analyze the linearized version of a poromechanics model developed to simulate biological tissues perfusion. This is a fully dynamical model in which the fluid and solid equations are strongly coupled through the interstitial pressure. As such, it generalizes Darcy, Brinkman and Biot equations of poroelasticity. The mathematical and numerical analysis of this model was first performed for a compressible porous material. Here, we focus on the nearly incompressible case with a semigroup approach that also enables to prove the existence of weak solutions. We show the existence and uniqueness of strong and weak solutions in the incompressible limit, for which a non-standard divergence constraint arises. Due to the special form of the coupling, the underlying problem is not coercive. Nevertheless, by using the notion of T-coercivity, we obtain stability estimates and well-posedness results. Our study also provides guidelines to propose a stable and robust approximation of the problem with mixed finite elements. In particular, we recover an inf-sup condition independent of the phase field. Finally, we investigate numerically the elliptic regularity of the associated steady-state problem and illustrate the sensitivity of the solution with respect to the different model parameters. (10.3934/eect.2022053)
  DOI : 10.3934/eect.2022053
• An efficient numerical method for time domain electromagnetic wave propagation in co-axial cables
  
  • Beni Hamad Akram
  • Beck Geoffrey
  • Imperiale Sébastien
  • Joly Patrick
  Computational Methods in Applied Mathematics, De Gruyter, 2022, 22 (4). In this work we construct an efficient numerical method to solve 3D Maxwell's equations in coaxial cables. Our strategy is based upon an hybrid explicit-implicit time discretization combined with edge elements on prisms and numerical quadrature. One of the objective is to validate numerically generalized Telegrapher's models that are used to simplify the 3D Maxwell equations into a 1D problem. This is the object of the second part of the article. (10.1515/cmam-2021-0195)
  DOI : 10.1515/cmam-2021-0195
• An assessment of anisotropic phase-field models of brittle fracture
  
  • Scherer Jean-Michel
  • Brach Stella
  • Bleyer Jeremy
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2022, 395, pp.115036. In several classes of ductile and brittle materials consisting of different cleavage planes, an orientation dependency of the fracture process is observed. It leads for instance to complex failure behaviours and crack paths in polycrystalline or architected materials. This paper focuses on modeling anisotropy of brittle fracture by means of a variational phase-field approach. More precisely, we study different models including several phase (or damage) variables corresponding to different damage mechanisms. First, we recall a multi-mechanism gradient damage model based on an anisotropic non-local fracture energy. We then consider a model accounting for an anisotropic degradation of the elasticity stiffness tensor. Both types of anisotropies are compared in terms of their influence on analytical homogeneous solutions under uniaxial and biaxial tensile loadings. Weak and strong anisotropies are captured via the chosen multi-mechanism damage framework. The models are implemented numerically by using a finite element discretization. In order to improve numerical performance, we implement an algorithm based on a hybrid direct-iterative resolution of the displacement sub-problem. Accuracy of model prediction is assessed by comparing numerical results to theoretical solutions under uniaxial loading. Benchmark numerical tests on notched and perforated plates highlight the role of material parameters on the fracture anisotropy. Furthermore, both models are able to retrieve zigzag crack patterns observed in prior numerical and experimental studies. Finally, we discuss the predictions of a model combining both types of anisotropies. (10.1016/j.cma.2022.115036)
  DOI : 10.1016/j.cma.2022.115036
• Special Issue of the VPH2020 Conference: “Virtual Physiological Human: When Models, Methods and Experiments Meet the Clinic”
  
  • Vignon-Clémentel Irène
  • Chapelle Dominique
  • Moireau Philippe
  • Barakat Abdul I.
  • Bel-Brunon A.
  • Vibert Eric
  Annals of Biomedical Engineering, Springer Verlag, 2022, 50 (5), pp.483-484. No abstract available (10.1007/s10439-022-02943-y)
  DOI : 10.1007/s10439-022-02943-y
• Analysis Of Real-Life Multi-Input Loading Histories For The Reliable Design Of Vehicle Chassis
  
  • Baroux Emilien
  • Delattre Benoit
  • Constantinescu Andrei
  • Pamphile Patrick
  • Raoult Ida
  Procedia Structural Integrity, ESIS - Elsevier, 2022, 38, pp.497-506. (10.1016/j.prostr.2022.03.050)
  DOI : 10.1016/j.prostr.2022.03.050
• A unified dual modeling framework for soft and hard magnetorheological elastomers
  
  • Mukherjee Dipayan
  • Danas Kostas
  International Journal of Solids and Structures, Elsevier, 2022. Most current magnetorheological elastomers (MREs) are broadly categorized into hard(h-MREs) and soft(s-MREs) depending on the magnetic properties of the underlying particles. The former consist of particles exhibiting strong magnetic dissipation (e.g., NdFeB), while the later are purely energetic (e.g., carbonyl iron). In this work, we present a unified modeling framework for h-MREs including the response of the s-MREs as a limiting case when the dissipation is set to zero. In addition, the proposed framework is dual in the sense of a partial Legendre-Fenchel transform of the magnetic part, i.e., we propose exactly equivalent models in the F − H and F − B variable spaces. Efficient finite element, numerical solutions for various boundary value problems (BVPs) involving hand s-MREs are obtained via incremental variational principles. The calculations for the end-tip deflection of a uniformly pre-magnetized cantilever exhibit excellent agreement with the experimental data. The investigations on the remanent fields and the magnetic actuation performance of hybrid h-/s-MRE rank-1 laminated cantilevers and non-uniformly pre-magnetized, functionally graded beams are also carried out. The analysis shows that pre-magnetization profiling of the h-MRE beams allows to program efficiently the deflection patterns upon subsequent application of a small actuating magnetic field. Furthermore, concentrating the hard-magnetic particles near the beam flanks reduces the actuation field considerably. The proposed F − H and F − B-based modeling frameworks and their numerical implementations serve as useful tools in analyzing the magneto-mechanical performance of the MRE structures made of sand h-MREs. (10.1016/j.ijsolstr.2022.111513)
  DOI : 10.1016/j.ijsolstr.2022.111513
• Insight on precipitate evolution during additive manufacturing of stainless steels via in-situ heating-cooling experiments in a transmission electron microscope
  
  • Ben Haj Slama Meriem
  • Yedra Lluis
  • Heripre Eva
  • Upadhyay Manas V
  Materialia, Elsevier, 2022. During additive manufacturing of alloys, just after local heat-matter interactions, a molten material undergoes rapid solidification. Then, for the rest of the building time, it is subjected to cooling/heating cycles in the solid-state i.e., solid-state thermal cycling. The thermo-mechanical forces generated during solid-state thermal cycling can trigger a plethora of micro-mechanisms that can bring about significant microstructural changes that determine the eventual mechanical properties of as-built parts. In this work, the aim is to gain insight on solid-state thermal cyclingdriven evolution of submicron-sized precipitates in an austenitic stainless steel using transmission electron microscopy. To that end, thin-film lamellae are extracted from a pre-built sample and subjected to different in-situ solid-state thermal cycles inside a transmission electron microscope. The solid-state thermal cycles are designed to understand the role of temperature amplitude and rates, number and type of thermal cycles, and post-process annealing on precipitate evolution. High angle annular dark field imaging and energy dispersive X-ray spectroscopy before and after each thermal cycle provide a deep insight on the contribution of different thermal cycling factors on the evolution of precipitate composition, size and morphology. Common trends include diffusion of Mn and Si from Mn-Si-rich oxides into the surrounding matrix, formation of Cr rings around oxide precipitates and S redistribution in non-oxide precipitates. Similar Cr rings and S distributions were also found in precipitates in as-built samples studied in (Upadhyay et al., Sci. Rep. 11 (2021) 10393), which strongly supports the representativeness of these results with respect to what occurs during additive manufacturing. (10.1016/j.mtla.2022.101368)
  DOI : 10.1016/j.mtla.2022.101368
• Analysis and fast modelling of microstructures in duplex stainless steel formed by directed energy deposition additive manufacturing
  
  • Edwards Alexander
  • Weisz-Patrault Daniel
  • Charkaluk Eric
  Additive Manufacturing, Elsevier, 2022, 61, pp.103300. The properties of duplex stainless steels depend strongly on their thermal history, which can produce a wide range of austenite to ferrite ratios; whereas optimal properties generally require near 50-50 ferrite-austenite duplex microstructures. Additive manufacturing processes of duplex steels remain challenging as it is difficult to predict and control how the phase ratio depends on process parameters. This paper focuses on directed energy deposition additive manufacturing and presents a fast numerical modelling of the thermal history and diffusion controlled solid-solid phase transformations in the entire part. The proposed simulations strategy is sufficiently fast to optimize the process parameters to achieve a targeted distribution of phase ratio, and a temperature control strategy of the build platform has been proposed on this basis to reach almost uniform near 50-50 phase ratios, which was obtained by setting the temperature profile of the build platform as a linear function decreasing from 1000~K for the first layer to 800~K for the last layer. In addition, experiments are conducted to validate the proposed approach. Microstructures and phase ratio gradients are assessed in single-bead-thickness walls of SAF~2507 superduplex stainless steel, and numerical results are in reasonable agreement with experimental observations. (10.1016/j.addma.2022.103300)
  DOI : 10.1016/j.addma.2022.103300
• Quantification of left ventricular strain and torsion by joint analysis of 3D tagging and cine MR images
  
  • Berberoğlu Ezgi
  • Stoeck Christian
  • Kozerke Sebastian
  • Genet Martin
  Medical Image Analysis, Elsevier, 2022. Cardiovascular magnetic resonance (CMR) imaging is the gold standard for the noninvasive assessment of left-ventricular (LV) function. Prognostic value of deformation metrics extracted directly from regular cine CMR images has been shown by numerous studies in the clinical setting, but with some limitations to detect torsion of the myocardium. Tagged CMR introduces trackable features in the myocardium that allow for the assessment local myocardial deformation, including torsion; it is, however, limited in the quantification of radial strain, which is a decisive metric for assessing the contractility of the heart. In order to improve cine-only and tagged-only approaches, we propose to combine the advantages of both image types by fusing global shape motion obtained from cine images with the local deformation obtained from tagged images. To this end, tracking is first performed on cine images, and subsequently, the resulting motion is utilized to mask and track tagged data. Our implementation is based on a recent finite element-based motion tracking tool with mechanical regularization. Joint cine and tagged images registration performance is assessed based on deformation metrics including LV strain and twist using human and in-house porcine datasets. Results show that joint analysis of cine and 3DTAG images provides better quantification of LV strain and twist as either data source alone. (10.1016/j.media.2022.102598)
  DOI : 10.1016/j.media.2022.102598
• Subsidence above rock-salt cavities - Numerical and explicit evaluations
  
  • Quintanilha de Menezes J. E.
  • Nguyen Minh D.
  , 2001, pp.139-143. Subsidence is always a long-term effect from the exploration of natural gas storage cavities. The internal pressure being less than in situ pressure leads to cavity convergence with has economical consequences as well as possible outcomes on the surface. After reviewing the subsidence phenomenology, by identifying what can be observed at the surface, and its environmental and structural consequences, some empirical and analytical means of estimating its deformation values are referred. With more detail, a numerical application is presented which uses coupled boundary and finite elements for subsidence evaluation due to deep storage cavities. This lasts characteristic gives rise to large extensions of deformed zones towards the surface. A real case of a storage cavity field with subsidence measurements made for more than ten years is taken as example and some predictions are made on future subsidence and horizontal displacement. (10.1201/9781003078562-16)
  DOI : 10.1201/9781003078562-16
• Modelling the fluid-structure interactions of a capsule using a nonlinear thin shell model: effect of wall thickness
  
  • Dupont Claire
  • Vidrascu Marina
  • Le Tallec Patrick
  • Barthès-Biesel Dominique
  • Salsac Anne-Virginie
  Journal of Fluids and Structures, Elsevier, 2022, 113 (103658). We address the question of the modelling of the fluid-structure interactions for a microcapsule enclosed by a finite-thickness wall, and of the prediction of the buckling behaviour when it is subjected to large displacements and deformations. Specifically, we model the strong coupling between the solid (the wall dynamics) and fluid (the flow inside and outside the capsule) mechanics, for a wall material that can be strain-hardening or softening, while accounting for the bending resistance due to thickness. The fluid flow is assumed to be inertialess on the capsule scale, which allows the use of the boundary integral formulation for the fluid velocity. We discuss the different simplifications that are made when designing a fluid-shell interaction model for large deformations, and present a shear-membrane-bending (SMB) shell model that allows for a nonlinear wall stretching law. The performance of the model, as compared to a simple membrane model where bending resistance is neglected, is illustrated on a generic example: we consider an initially ellipsoidal capsule, freely suspended in a plane hyperbolic flow, that is subjected to such stringent deformation, that its short axis becomes the long one. We show that the simple membrane model predicts reasonably well the overall shape of the capsule, but cannot capture the detailed post buckling behaviour, for which a robust shell model is necessary. The SMB shell model complies with dominant membrane effects, remains stable even under large deformation and avoids numerical locking. It allows predicting post-buckling behaviour, which depends on the material constitutive law. (10.1016/j.jfluidstructs.2022.103658)
  DOI : 10.1016/j.jfluidstructs.2022.103658
• Physically-based sound synthesis software for Computer-Aided-Design of piano soundboards
  
  • Elie Benjamin
  • Cotté Benjamin
  • Boutillon Xavier
  Acta Acustica, EDP Sciences, 2022, 6, pp.30. The design of pianos is mainly based on empirical knowledge due to the lack of a simple tool that could predict sound changes induced by modifications of the geometry and/or the mechanical properties of the soundboard. We introduce the concept of Sound Computer-Aided Design through the framework of a program that is intended to simulate the acoustic results of virtual pianos. The calculation of the sound is split into four modules that compute respectively the modal basis of the stiffened soundboard, the string dynamics excited by the hammer, the soundboard dynamics excited by the string vibration, and the sound radiation. The exact resemblance between synthesis and natural sounds is not the primary purpose of the software. However, sound synthesis of real and modified pianos are used as reference tests to assess our main objective, namely to reflect faithfully structural modifications in the produced sound, and thus to make this tool helpful for both instrument makers and researchers of the musical acoustics community. (10.1051/aacus/2022024)
  DOI : 10.1051/aacus/2022024
• Single-lap joint creep behaviour of two soft adhesives
  
  • Ernault Estève
  • Diani Julie
  • Schmid Quentin
  The Journal of Adhesion, Taylor & Francis, 2022. Two hot melt pressure sensitive adhesives have been submitted to bonded joint creep tests. An amorphous and a semicrystalline adhesives have been considered for their different microstructures leading to different mechanical behaviors. The adhesives are referred as soft since their glass transition temperatures stand well below the temperatures of applications, resulting in low stiffnesses. The creep of structural joints has been characterized with single-lap joint tests. Two types of adherends were considered either glass or stainless steel. The adherend roughness and the adhesive wettability have been characterized before testing. The significant stiffness contrast between the stiff adherends and the soft adhesives promoted homogeneous simple shear creeps. The amorphous adhesive showed creep behaviors that depend on the type of substrates, showing that the joint viscoelasticity could not be predicted knowing the bulk adhesive viscoelasticity only, unlike for stiff adhesives as recently reported in the literature. Finally, the SLJ creep behaviors of both adhesives on the same glass adherends were compared and discussed at the light of their different microstructures inducing different mechanical behaviors. (10.1080/00218464.2022.2100254)
  DOI : 10.1080/00218464.2022.2100254
• Mechanical behavior of surface-patterned and coated Si or Ge wafers for superhydrophobic and antireflective light transmitting windows
  
  • Doquet Véronique
  • Tanguy Alexandre
  • Hallais Simon
  • Guillemet Raphaël
  • Cholet Julie
  • Jussey Doriane
  Journal of Materials Science, Springer Verlag, 2022. The compressive resistance of truncated nanocone lattices produced by lithography and etching steps on Si or Ge wafers to get superhydrophobic and antireflective light transmitting windows, as well as the protection efficiency of alumina or diamond coatings are investigated by numerical simulations of elastic buckling, and nano-compression tests. The latter reveal the limits of an elastic analysis, since the stress at the top of the cones is high enough to trigger plastic flow, or phase changes. Ge nano-cones exhibit a large ductility in compression, and even seem to creep at room temperature. Thin alumina or diamond coatings are however shown to provide an effective protection against both buckling and plastic flow. Surface patterning is shown to induce stress concentrations at the foot of the cones, which reduces the fracture resistance of the substrate in biaxial bending. (10.1007/s10853-021-06794-1)
  DOI : 10.1007/s10853-021-06794-1
• Mechanofluorochromic Difluoroboron <i>β</i> ‐Diketonates Based Polymer Composites: Toward Multi‐Stimuli Responsive Mechanical Stress Probes
  
  • Poggi Benjamin
  • Lopez Elliot
  • Métivier Rémi
  • Bodelot Laurence
  • Allain Clémence
  Macromolecular Rapid Communications, Wiley-VCH Verlag, 2022, 43 (15), pp.2200134. Developing mechano-responsive fluorescent polymers that exhibit distinct responses to distinct mechanical stresses requires a careful design of the fluorophore in order to tune its interactions with the polymer. A series of mechanofluorochromic (MFC) polymer composites are prepared by dispersing difluoroboron diketonates complexes with various alkyl side-chain lengths (DFB-alkyl) in linear low-density polyethylene. Observation of the resulting polymer composites under a microscope reveals different aggregate sizes of the three DFB-alkyls, thus confirming the functionalization by alkyl side chains as a powerful approach to control the aggregation process in a polymer. Besides, the three polymer composite samples are shown to be sensitive to both stretching and scratching, thereby consisting in the first reported example of MFC polymer responding to these two distinct mechanical stimuli. To establish a structure-property relationship, the strategy consisted in applying controlled tensile or friction forces while simultaneously monitoring fluorescence changes. Interestingly, the intensity of the MFC response to both stretching and scratching depends on the alkyl chain length and thus on the aggregation properties of the fluorophore. According to a time-resolved fluorescence study, the emission is found to originate from different species following the type of applied stress (tensile or friction force). (10.1002/marc.202200134)
  DOI : 10.1002/marc.202200134
• Three-dimensional X-FEM modeling of crack coalescence phenomena in the Smart Cut™ technology
  
  • Pali E.
  • Gravouil A.
  • Tanguy A.
  • Landru D.
  • Kononchuk O.
  Finite Elements in Analysis and Design, Elsevier, 2022, 213. A new 3D X-FEM approach is proposed to model crack coalescence phenomena in the Smart Cut (TM) technology. An adaptive mesh is developed based on a 3D fractal mesh allowing a significant gain in computing time compared to regular meshes. In order to calculate stress intensity factors (SIFs), the term corresponding to internal pressure, that is normal loading on crack faces has been determined, added to the interaction integral and the results of SIFs in mode I have been compared to their analytical values with mean error less than 1%. An implicit algorithm is implemented to predict the evolution of the internal pressure for growing cracks of any shape; a constitutive law in pressure correlated with the equation of state of ideal gases has therefore been used. Compared to the analytical solution, numerically evaluated pressure is accurate with maximum errors less than 1% for relevant convergence tolerance. Finally, the coalescence of two cracks is taken into account in the model. Qualitative local stress analysis makes it possible to explain some phenomena experimentally observed in the Smart Cut (TM) such as neighboring effects of growing cracks, the outgrowth of nearby cracks or influence of the presence of concave areas at a front on growth. (10.1016/j.finel.2022.103839)
  DOI : 10.1016/j.finel.2022.103839
• A generic topography reconstruction method based on multi-detector back scattered electron images
  
  • Neggers Jan
  • Héripré Eva
  • Bonnet Marc
  • Hallais Simon
  • Roux Stéphane
  Strain, Wiley-Blackwell, 2022, 58 (5), pp.1625-1646. Surface topographies can be reconstructed from backscattered electron (BSE) images captured from different detector orientations. This article presents a very general approach to this problem, in the spirit of photometric stereo methods, allowing for arbitrary BSE detector number (at least 3) and shapes. The general idea is to both determine the (non‐linear) model parameters and compute the surface topography so that the modelled images match at best the acquired ones. Three samples are used for validation of the measured topography with respect to atomic force microscopy (AFM) measurements. Root mean square (RMS) errors in the range of 10–35 nm, or 1–1.5% of total sampleheight, are obtained. (10.1111/str.12416)
  DOI : 10.1111/str.12416