Publications

2021

• Deformation of aluminum in situ SEM and full field measurements by digital image correlation: evidence of concomitant crystal slip and grain boundary sliding
  
  • Dimanov A
  • Sabbagh A El
  • Raphanel J
  • Lê T N
  • Bornert Michel
  • Hallais S
  • Tanguy A
  , 2021. Mechanical testing in situ scanning electron microscopy (SEM) has become a current technique for multiscale micromechanical investigation of polycrystalline materials, because direct observation of deformation microstructures allows identification of strain heterogeneities and related mechanisms. Yet, most of the studies are based on the inherited post mortem microstructures, thus precluding to unravel the local loading history, to understand the development of localization patterns, the potential interactions of concomitant mechanisms and to quantify their respective contributions to the overall strain. We therefore developed a novel experimental setup for thermomechanical testing in situ SEM, especially suited for full strain field measurements based on digital image correlation (DIC) from the sample scale, to the scales of the aggregate and the single grain. We present results obtained during simple compression, at controlled displacement rate and at temperatures up to 400°C, for polycrystalline aluminum presenting randomly oriented coarse grains (ca. 300 m in size). According to the different scales of interest, specific surface marking patterns were realized by electron microlithography. Kinematic analysis by digital image correlation (DIC) allowed to retrieve full surface strain fields. The latter evidenced that the overall viscoplastic response was dominated by crystal slip plasticity. Increasing temperature favored the activation of non-octahedral slip, but also substantial and continuous contribution of grain boundary sliding (GBS). We suggest the latter mechanism as necessary to accommodate local plastic incompatibilities between neighboring grains.
• Application of mechanochemistry model to oxidation of pure nickel spheres
  
  • Petrenko Svetlana
  • Charkaluk Eric
  • Tanguy Alexandre
  • Davoine Cecile
  , 2021, pp.P108205. In this work, we study the two-phase chemical reactions on the example of the oxidation of nickel. We have carried out an experiment of high-temperature oxidation of nickel balls, and obtained the experimental data for the growth of the oxide layer over time. To select the best analytical solution we consider three different rheology for the oxide of nickel: elastic, elastoplastic and viscoelastic. We compare the solution for each rheological model with experimental data.
• Revisiting step instabilities on crystal surfaces. Part I: The quasistatic approximation
  
  • Guin Laurent
  • Jabbour M.E.
  • Triantafyllidis N.
  Journal of the Mechanics and Physics of Solids, Elsevier, 2021, 156, pp.104574. Epitaxial growth on a surface vicinal to a high-symmetry crystallographic plane occurs through the propagation of atomic steps, a process called step-flow growth. In some instances, the steps tend to form close groups (or bunches), a phenomenon termed step bunching, which corresponds to an instability of the equal-spacing step propagation. Over the last fifty years, various mechanisms have been proposed to explain step bunching, the most prominent of which are the inverse Ehrlich-Schwoebel effect (i.e., the asymmetry which favors the attachment of adatoms from the upper terrace), elastically mediated interactions between steps (in heteroepitaxy), step permeability (in electromigration-controlled growth), and the chemical effect (which couples the diffusion fields on all terraces). Beyond the discussion of the influence of each of these mechanisms taken independently on the propensity to bunching, we propose a unified treatment of the effect of these mechanisms on the onset of the bunching instability, which also accounts for their interplay. This is done in the setting of the so-called quasistatic approximation, which by permitting mostly analytical treatment, offers a clear view of the influence on stability of the combined mechanisms. In particular, we find that the Ehrlich-Schwoebel effect, elastic step-interactions and the chemical effect combine in a quasi-additive fashion, whereas step permeability is neither stabilizing nor destabilizing per se but changes the relative influence of the three aforementioned mechanisms. In a companion paper, we demonstrate and discuss the importance of another mechanism, which we call the dynamics effect, that emerges when relaxing the simplifying but questionable quasistatic approximation. (10.1016/j.jmps.2021.104574)
  DOI : 10.1016/j.jmps.2021.104574
• Principal image decomposition for multi-detector backscatter electron topography reconstruction
  
  • Neggers Jan
  • Héripré Eva
  • Bonnet Marc
  • Boivin Denis
  • Tanguy Alexandre
  • Hallais Simon
  • Gaslain Fabrice
  • Rouesne Elodie
  • Roux Stéphane
  Ultramicroscopy, Elsevier, 2021, 227, pp.113200. Scanning Electron Microscopes (SEMs) often generate images with a shaded appearance which gives a natural 3D impression. Ergo, quite a few methods to reconstruct the 3D surface topography from these using shape-from-shading methods are available in the literature. Here, a novel approach is discussed which uses BackScatter Electron (BSE) images from multiple detectors to reconstruct the topography. Classically, algorithms exist which resort to a quad-BSE detector setup. However, other detector configurations are often found in SEMs. A set of images of these non-conforming detectors still contains enough information to allow for reconstruction, but requires a more general algorithm to do so. This article discusses a method based on a modal decomposition of the principal image components. The resulting method is shown to be efficient and independent of the number of detectors or their orientation. In fact, the orientation is identified as part of the algorithm and thus requires very little calibration. (10.1016/j.ultramic.2020.113200)
  DOI : 10.1016/j.ultramic.2020.113200
• Revisiting step instabilities on crystal surfaces. Part II: General theory
  
  • Guin Laurent
  • Jabbour Michel E.
  • Shaabani-Ardali Leopold
  • Triantafyllidis Nicolas
  Journal of the Mechanics and Physics of Solids, Elsevier, 2021, 156, pp.104582. The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on stability of different mechanisms and their interplay: elastic step-step interactions, the Schwoebel barrier, and the chemical coupling of the diffusion fields on adjacent terraces. In this second part, we present a stability analysis of the general problem without recourse to the quasistatic approximation. This analysis reveals the existence of a supplementary mechanism, which we label the "dynamics effect" as it follows from accounting for all the convective and transient terms in the governing equations. This effect can be stabilizing or destabilizing depending on the ratio of step attachment/detachment kinetics to terrace diffusion kinetics. Further, we find that this dynamics effect remains significant in the slow deposition/evaporation regime, thereby invalidating the classical postulate underlying the quasistatic approximation. Finally, revisiting experiments of crystal growth on Si(111)-7 × 7 and GaAs(001), our analysis provides an alternative explanation of the observed step bunching, one that does not require the mechanisms previously invoked in the literature. (10.1016/j.jmps.2021.104582)
  DOI : 10.1016/j.jmps.2021.104582
• Hierarchical modeling of length-dependent force generation in cardiac muscles and associated thermodynamically-consistent numerical schemes
  
  • Kimmig François
  • Moireau Philippe
  • Chapelle Dominique
  Computational Mechanics, Springer Verlag, 2021, 68, pp.885–920. In the context of cardiac muscle modeling, the availability of the myosin heads in the sarcomeres varies over the heart cycle contributing to the Frank-Starling mechanism at the organ level. In this paper, we propose a new approach that allows to extend the Huxley'57 muscle contraction model equations to incorporate this variation. This extension is built in a thermodynamically consistent manner, and we also propose adapted numerical methods that satisfy thermodynamical balances at the discrete level. Moreover, this whole approach-both for the model and the numerics-is devised within a hierarchical strategy enabling the coupling of the microscopic sarcomere-level equations with the macroscopic tissue-level description. As an important illustration, coupling our model with a previously proposed simplified heart model, we demonstrate the ability of the modeling and numerical framework to capture the essential features of the Frank-Starling mechanism. (10.1007/s00466-021-02051-z)
  DOI : 10.1007/s00466-021-02051-z
• On the dynamic behaviour of discrete metamaterials: From attenuation to energy localization
  
  • Moscatelli Marco
  • Comi Claudia
  • Marigo Jean-Jacques
  Wave Motion, Elsevier, 2021, 104, pp.102733. (10.1016/j.wavemoti.2021.102733)
  DOI : 10.1016/j.wavemoti.2021.102733
• A 3D personalized cardiac myocyte aggregate orientation model using MRI data-driven low-rank basis functions
  
  • Stimm Johanna
  • Buoso Stefano
  • Berberoğlu Ezgi
  • Kozerke Sebastian
  • Genet Martin
  • Stoeck Christian
  Medical Image Analysis, Elsevier, 2021, 71, pp.102064. (10.1016/j.media.2021.102064)
  DOI : 10.1016/j.media.2021.102064
• Pince optique pour la micro-rhéologie des caillots sanguins
  
  • Westbrook Nathalie
  • Moreau Julien
  • Wolff Laura
  • Allain Jean-Marc
  • James Chloé
  , 2021.
• Combining Data Assimilation and Machine Learning to build data-driven models for unknown long time dynamics - Applications in cardiovascular modeling
  
  • Regazzoni Francesco
  • Chapelle Dominique
  • Moireau Philippe
  International Journal for Numerical Methods in Biomedical Engineering, John Wiley and Sons, 2021, 37 (7). We propose a method to discover differential equations describing the long-term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast-scale. Our methodology is based on a synergetic combination of Data Assimilation (DA), used to estimate the parameters associated with the known fast-scale dynamics, and Machine Learning (ML), used to infer the laws underlying the slow-scale dynamics. Specifically, by exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden. Then, we propose a ML algorithm that learns a parametric mathematical model from a collection of time series coming from the phenomenon to be modeled. Moreover, we study the interpretability of the data-driven models obtained within the black-box learning framework proposed in this paper. In particular, we show that every model can be rewritten in infinitely many different equivalent ways, thus making intrinsically ill-posed the problem of learning a parametric differential equation starting from time series. Hence, we propose a strategy that allows to select a unique representative model in each equivalence class, thus enhancing the interpretability of the results. We demonstrate the effectiveness and noise-robustness of the proposed methods through several test cases, in which we reconstruct several differential models starting from time series generated through the models themselves. Finally, we show the results obtained for a test case in the cardiovascular modeling context, which sheds light on a promising field of application of the proposed methods. (10.1002/cnm.3471)
  DOI : 10.1002/cnm.3471
• Multiscale experimental and theoretical investigation of the structure-property relationships in the myocardium
  
  • Tueni Nicole
  , 2021. The myocardium is a complex tissue, primarily made of cardiac cells and extra-cellular collagenous matrix, arranged in a hierarchical microstructure. This microstructure evolves with time, either physiologically or pathologically, altering the macroscopic mechanical properties of heart, hence its function. The objective of this PhD thesis is to improve our understanding of the structure-properties relationships in the cardiac tissue by focusing on the role of mesostructure, called the sheetlet, on the macroscopic mechanical properties. In a first part, a literature review of the existing literature on the role of sheetlet is performed. In the second chapter, we present an experimental setup we developed, combining a full-field Mueller polarimetric imager and an in-situ traction device with a local measure of the deformation during sample stretch. We observe a global cohesion of the tissue apart on separation lines at the mesoscale, that tend to open under traction. We hypothesize that these lines are the collageneous layers separating the sheetles, bundles of cardiomyocytes surrounded by layers of perimysial collagen. In the third chapter, we propose a simple optical method combined with a fast image analysis to extract the sheetlet local orientation on left ventricle slices, in order to construct a 3D mapping of the sheetlet organization in the heart. In the second part of the PhD thesis (chapter four), we propose a multiscale model of the myocardium aiming at determining the structural origin of the observed macroscale mechanical anisotropy. Indeed, the observed orthotropy can be due either to the rotation of the cell orientation, or to the presence of the mesoscale collageneous layers. We design three mesostructures made of different configurations of cardiomyocytes and collagen. The mechanical response of these mesostructures are homogenized with numerical periodic homogenization, and the obtained material parameters are used in a macroscopic simulation of a shear experiment. The comparison between our results and the experimental data show that the collagen layers are necessary to reproduce the material orthotropy. The final chapter of this thesis presents some perspectives of this work.
• Construction and convergence analysis of conservative second order local time discretisation for linear wave equations
  
  • Chabassier Juliette
  • Imperiale Sébastien
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2021, 55 (4), pp.1507-1543. In this work we present and analyse a time discretisation strategy for linear wave equations t hat aims at using locally in space the most adapted time discretisation among a family of implicit or explicit centered second order schemes. The proposed family of schemes is adapted to domain decomposition methods such as the mortar element method. They correspond in that case to local implicit schemes and to local time stepping. We show that, if some regularity properties of the solution are satisfied and if the time step verifies a stability condition, then the family of proposed time discretisations provides, in a strong norm, second order space-time convergence. Finally, we provide 1D and 2D numerical illustrations that confirm the obtained theoretical results and we compare our approach on 1D test cases to other existing local time stepping strategies for wave equations. (10.1051/m2an/2021030)
  DOI : 10.1051/m2an/2021030
• Model-Assisted Time-Synchronization of Cardiac MR Image and Catheter Pressure Data
  
  • Gusseva Maria
  • Greer Joshua S
  • Castellanos Daniel A
  • Abdelghafar Hussein Mohamed
  • Greil Gerald
  • Veeram Reddy Surendranath R
  • Hussain Tarique
  • Chapelle Dominique
  • Chabiniok Radomir
  , 2021, pp.362-372. When combining cardiovascular magnetic resonance imaging (CMR) with pressure catheter measurements, the acquired imageand pressure data need to be synchronized in time. The time offset between the image and pressure data depends on a number of factors,such as the type and settings of the MR sequence, duration and shape of QRS complex or the type of catheter, and cannot be typically estimated beforehand. In the present work we propose using a biophysical heart model to synchronize the left ventricular (LV) pressure and volume (P-V) data. Ten patients, who underwent CMR and LV catheterization, were included. A biophysical model of reduced geometrical complexity with physiologically substantiated timing of each phase of the cardiac cycle was first adjusted to individual patients using basic morphological and functional indicators. The pressure and volume waveforms simulated by the patient-specific models were then used as templates to detect the time offset between the acquired ventricular pressure and volume waveforms. Time-varying ventricular elastance was derived from clinical data both as originally acquired as well as when time-synchronized, and normalized with respect to end-systolic time and maximum elastance value$E^N_\text {orig}(t)$, $E^N_\text {t-syn}(t)$, respectively). $E^N_\text {t-syn}(t)$ was significantly closer to the experimentally obtained $E^N_\text {exp}(t)$ published in the literature (p < 0.05, $L^2$ norm). The work concludes that the model-driven time-synchronization of P-V data obtained by catheter measurement and CMR allows to generate high quality P-V loops, which can then be used for clinical interpretation. (10.1007/978-3-030-78710-3_35)
  DOI : 10.1007/978-3-030-78710-3_35
• Unique and universal dew-repellency of nanocones
  
  • Lecointre Pierre
  • Laney Sophia
  • Michalska Martyna
  • Li Tao
  • Tanguy Alexandre
  • Papakonstantinou Ioannis
  • Quéré David
  Nature Communications, Nature Publishing Group, 2021, 12 (1). Surface structuring provides a broad range of water-repellent materials known for their ability to reflect millimetre-sized raindrops. Dispelling water at the considerably reduced scale of fog or dew, however, constitutes a significant challenge, owing to the comparable size of droplets and structures. Nonetheless, a surface comprising nanocones was recently reported to exhibit strong anti-fogging behaviour, unlike pillars of the same size. To elucidate the origin of these differences, we systematically compare families of nanotexture that transition from pillars to sharp cones. Through environmental electron microscopy and modelling, we show that microdroplets condensing on sharp cones adopt a highly non-adhesive state, even at radii as low as 1.5 µm, contrasting with the behaviour on pillars where pinning results in impedance of droplet ejection. We establish the antifogging abilities to be universal over the range of our cone geometries, which speaks to the unique character of the nanocone geometry to repel dew. Truncated cones are finally shown to provide both pinning and a high degree of hydrophobicity, opposing characteristics that lead to a different, yet efficient, mechanism of dew ejection that relies on multiple coalescences. (10.1038/s41467-021-23708-6)
  DOI : 10.1038/s41467-021-23708-6
• An explicit dissipative model for isotropic hard magnetorheological elastomers
  
  • Mukherjee Dipayan
  • Rambausek Matthias
  • Danas Kostas
  Journal of the Mechanics and Physics of Solids, Elsevier, 2021, 151, pp.104361. Hard magnetorheological elastomers (h-MREs) are essentially two phase composites comprising permanently magnetizable metallic inclusions suspended in a soft elastomeric matrix. This work provides a thermodynamically consistent, microstructurally-guided modeling framework for isotropic, incompressible h-MREs. Energy dissipates in such hardmagnetic composites primarily via ferromagnetic hysteresis in the underlying hard-magnetic particles. The proposed constitutive model is thus developed following the generalized standard materials framework, which necessitates suitable definitions of the energy density and the dissipation potential. Moreover, the proposed model is designed to recover several well-known homogenization results (and bounds) in the purely mechanical and purely magnetic limiting cases. The magneto-mechanical coupling response of the model, in turn, is calibrated with the aid of numerical homogenization estimates under symmetric cyclic loading. The performance of the model is then probed against several other numerical homogenization estimates considering various magneto-mechanical loading paths other than the calibration loading path. Very good agreement between the macroscopic model and the numerical homogenization estimates is observed, especially for stiff to moderately-soft matrix materials. An important outcome of the numerical simulations is the independence of the current magnetization to the stretch part of the deformation gradient. This is taken into account in the model by considering an only rotation-dependent remanent magnetic field as an internal variable. We further show that there is no need for an additional mechanical internal variable. Finally, the model is employed to solve macroscopic boundary value problems involving slender h-MRE structures and the results match excellently with experimental data from literature. Crucial differences are found between uniformly and non-uniformly pre-magnetized h-MREs in terms of their pre-magnetization and the associated self-fields. (10.1016/j.jmps.2021.104361)
  DOI : 10.1016/j.jmps.2021.104361
• Pseudo-compressibility, dispersive model and acoustic waves in shallow water flows
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Bristeau Marie-Odile
  • Godlewski Edwige
  • Imperiale Sébastien
  • Mangeney Anne
  • Sainte-Marie Jacques
  SEMA SIMAI Springer Series, Springer International Publishing, 2021, pp.209--250. In this paper we study a dispersive shallow water type model derived from the free surface compressible Navier-Stokes system. The compressible effects allow to capture the acoustic-like waves propagation and can be seen as a relaxation of an underlying incompressible model. The first interest of such a model is thus to capture both acoustic and water waves. The second interest lies in its numerical approximation. Indeed, at the discrete level, the pseudo-compressibility terms circumvent the resolution of an elliptic equation to capture the non-hydrostatic part of the pressure. This drastically reduces the cost of the numerical resolution of dispersive models especially in 2d and 3d. (10.1007/978-3-030-72850-2_10)
  DOI : 10.1007/978-3-030-72850-2_10
• A Comparative Study on Phonon Spectrum and Thermal Properties of Graphene, Silicene and Phosphorene: Recent Advances and Development
  
  • Kumar Arun
  • Devi Anjna
  • Singh Amarjeet
  • Ahluwalia P K
  , 2021, pp.93-99. On the basis of first-principle calculation using density functional theory, we systematically investigate the vibrational properties and thermal properties of two-dimensional honeycomb lattices of graphene, silicene and black phosphorene. We focus on the similarities and differences of their properties and try to understand them from their lattice structures. We illustrate that, a phonon band gap develops in silicene and black phosphorene which reduce effectively the phonon thermal conductivity. All the systems (graphene, silicene and black phosphorene) have positive frequencies which ensure their structural stability. Also, we found that the specific heat, entropy and free energy for all the systems increases rapidly at very low temperature and specific heat (Cv) become constant at higher temperature.
• Contraintes résiduelles et évolutions microstructurales dans les procédés de fabrication et de mise en forme
  
  • Weisz-Patrault Daniel
  , 2021. Dans cette présentation générale, je passe en revue l'ensemble des travaux, que j'ai menés depuis la fin de mon doctorat, pour donner un aperçu de la diversité des sujets et des approches utilisées (méthodes inverses, calculs analytiques, optimisations numériques, thermodynamique et approches énergétiques, statistiques Bayésiennes etc.). Par ailleurs, j'essaie de mettre en valeur et de rendre claire la structure globale, qui donne une cohérence à cet ensemble de travaux. En effet, l'ambition de ce mémoire n'est pas de détailler un domaine particulier, avec une longue présentation pédagogique de l'état de l'art. Je vise d'avantage à donner à voir, de manière synthétique et organisée, le cheminement de mon parcours de recherche et ma volonté d'aborder des sujets variés avec un regard que j'espère original, mais parfois naïf aussi probablement. Les enjeux de recherche, les idées principales et les méthodes seront évoqués, ainsi que les résultats intéressants. En revanche, compte tenu du caractère synthétique de cette présentation, je ne détaillerai pas les calculs théoriques de chacun des sujets. Pour cela, le lecteur pourra se reporter aux articles publiés. Par ailleurs, pour faciliter la lecture, les références sont triées par chapitre et séparées selon que j'en suis co-auteur ou non. Mes travaux sont principalement axés sur l'évaluation des contraintes résiduelles et de l'évolution de la microstructure dans les métaux (et plus particulièrement les aciers) à l'issue de différents procédés de mise en forme ou de fabrication. Mes recherches visent donc à offrir des outils pour une meilleure compréhension des conditions essentielles dans lesquelles se forment les contraintes résiduelles et les microstructures qui sous-tendent très largement le comportement macroscopique des matériaux. Ce cadre général se décline en différents axes~: (axe~1) méthodes inverses en temps réel (pour l'estimation de conditions inaccessibles dans des procédés), (axe~2) simulations rapides des procédés en considérant de nombreux couplages (mécanique, thermique, transition de phase, contacts mécaniques, etc.) et (axe~3) modèles théoriques macroscopiques conservant des informations provenant de la microstructure (transformations de phase, recristallisation, croissance de grain etc.). Cela permet d'intégrer, au niveau macroscopique, des phénomènes traversant les échelles (atomique, polycristalline et milieu continu). Par exemple, ces modèles cherchent à conserver à l'échelle du milieu continu, l'évolution statistique de la microstructure (arrangement cristallin, désorientation entre les grains, morphologie). Un quatrième axe s'ajoute à cette perspective globale : (axe~4) caractérisation des matériaux en dynamique, incluant les sources d'incertitudes. La conclusion de ce mémoire sera l'occasion de détailler mon projet de recherche pour les années à venir.
• Energetic upscaling strategy for grain growth. II: Probabilistic macroscopic model identified by Bayesian techniques
  
  • Weisz-Patrault Daniel
  • Sakout Sofia
  • Ehrlacher Alain
  Acta Materialia, Elsevier, 2021. This paper is the second part of an energetic upscaling strategy to simulate grain growth at the macroscopic scale with state variables that contain statistical descriptors of the grain structure. The first part was dedicated to the derivation of a fast mesoscopic model of grain growth based on oriented tessellation updating method, which consists in a succession of Voronoi-Laguerre tessellations obtained by establishing an evolution law directly on the parameters defining the tessellations. In this contribution, the final step of the upscaling strategy is detailed by deriving macroscopic evolutions laws of the state variables representing statistical distributions of the grain structure. The approach relies on macroscopic free energy and dissipation potentials that are identified not axiomatically with experimental calibration, but using a large database of mesoscopic computations. The macroscopic energy is found to be purely deterministic, although the dissipation necessitates to introduce a probabilistic framework. Indeed, an epistemic uncertainty arises due to the loss of information in the reduction of the amount of data between the detailed mesoscopic state and the statistical macroscopic state (i.e., several mesoscopic states can share the same macroscopic state). Classical Bayesian inference has been used to identify the probability density functions associated to the epistemic uncertainty. The resulting stochastic macroscopic model has been compared to several particular mesoscopic evolutions, and good agreement is observed. Thus, this work can be used to simulate grain growth at very large scale with short computation time, while processing rich statistical information about the grain structure, such as mean and standard deviation of the boundary misorientation distribution, grain boundary length density or grain size. (10.1016/j.actamat.2021.116805)
  DOI : 10.1016/j.actamat.2021.116805
• Relationship between microstructure and mechanical properties of polyether block amide foams
  
  • Ernault Estève
  • Diani Julie
  • Hallais Simon
  • Cocquet Clio
  Polymer Engineering and Science, Wiley-Blackwell, 2021, 61 (7), pp.1971 - 1981. The mechanical behaviors of five polyether block amide foams, obtained by mold-opening foam injection process, were investigated with regard to their microstructures. The materials vary in mass ratios of hard versus soft segments, and/or in process packing time. The resulting microstructures have been characterized in terms of cavity size and shape ratios, by analyzing scanning electron microscope images after careful sample preparation. The foam mechanical responses have been characterized in compression at small and large strain. At small strain, the initial linear part of the stress-strain curve is enhanced firstly by the hard segment mass ratio and secondly by the fineness of the microstructure. Similar results have been obtained at large strain. The foam viscoelasticity at large strain has been characterized by stress relaxation and strain recovery tests, relevant for foam applications. Reduced packing time and pressure have been shown to lead to the presence of undesired large cavities. The morphological defects appear to have a negligible impact on the macroscopic mechanical behavior of the foams at infinitesimal strain, but lead to critical inconsistency at large strain. Furthermore, the mechanical behavior of the tested polyether block amide foams is controlled first by hard vs. soft segments ratio, and second by the microstructure fineness (10.1002/pen.25712)
  DOI : 10.1002/pen.25712
• A one-dimensional model for elastic ribbons: a little stretching makes a big difference
  
  • Audoly Basile
  • Neukirch Sébastien
  Journal of the Mechanics and Physics of Solids, Elsevier, 2021, 153, pp.104457. Starting from the theory of elastic plates, we derive a non-linear one-dimensional model for elastic ribbons with thickness t, width a and length ℓ, assuming t≪a≪ℓ. It takes the form of a rod model with a special non-linear constitutive law accounting for both the stretching and the bending of the ribbon mid-surface. The model is asymptotically correct and can handle finite rotations. Two popular theories can be recovered as limiting cases, namely Kirchhoff's rod model for small bending and twisting strains, |κ_i|≪t/a^2, and Sadowsky's inextensible ribbon model for |κ_i|≫t/a^2; we point out that Sadowsky's inextensible model may be a poor approximation even for ribbons having a very thin cross-section, a/t∼50≫1. By way of illustration, the one-dimensional model is applied (i) to the lateral-torsional instability of a ribbon, showing good agreement with both experiments and finite-element shell simulations, and (ii) to the stability of a twisted ribbon subjected to a tensile force. The non-convexity of the one-dimensional model is discussed; it is addressed by a convexification argument. (10.1016/j.jmps.2021.104457)
  DOI : 10.1016/j.jmps.2021.104457
• Bending Response of a Book with Internal Friction
  
  • Audoly Basile
  • Poincloux Samuel
  • Chen Tian
  • Reis Pedro
  • Chen Tim
  Physical Review Letters, American Physical Society, 2021, 126 (21). We study the bending of a book-like system, comprising a stack of elastic plates coupled through friction. The behavior of this layered system is rich and nontrivial, with a non-additive enhancement of the apparent stiffness and a significant hysteretic response. A dimension reduction procedure is employed to develop a centerline-based theory describing the stack as a non-linear planar rod with internal shear. We consider the coupling between the nonlinear geometry and the elasticity of the stacked plates, treating the interlayer friction perturbatively. This model yields predictions for the stack's mechanical response in three-point bending that are in excellent agreement with our experiments. Remarkably, we find that the energy dissipated during deformation can be rationalized over three orders of magnitude, including the regimes of a thick stack with large deflection. This robust dissipative mechanism could be harnessed to design new classes of low-cost and efficient damping devices. (10.1103/PhysRevLett.126.218004)
  DOI : 10.1103/PhysRevLett.126.218004
• DIRECT MONITORING OF TWINNING/DETWINNING IN A TWIP STEEL UNDER REVERSED CYCLIC LOADING
  
  • d'Hondt C.
  • Doquet V.
  • Couzinié J.P. P
  Materials Science and Engineering: A, Elsevier, 2021, 814, pp.141250. In situ tensile and reversed cyclic tests were run on a TWIP steel in a SEM, with High-Resolution Digital Image Correlation (HR-DIC) measurements of the plastic strain field in a few selected grains prone to twinning, with a spatial resolution between 150 and 250nm, or under an AFM, with measurements of surface steps height at emerging deformation twins. Evidences of detwinning upon load reversal, as well as quantitative data on twinning/detwinning/retwinning were obtained. Detwinning and retwinning, which often were only partial, in spite of a fully reversed loading, did not seem to start at the onset of stress reversal. It required a sufficient variation of the stress, close to the twinning stress (estimated as 400 to 475 MPa) in absolute value, so that a mechanical hysteresis of the local twinned fraction occurred. Primary and secondary twinning along the same plane, inducing axial plastic strains in opposite directions, also allowed some grains to accommodate reversed plastic strain. Under fixed stress amplitude (± 500 MPa), the twin fraction in all monitored grains saturated at values between 0.5 and 3.5%, from the 2 nd cycle, while under fixed plastic strain amplitude (± 0.5%), it increased in a ratchetting way during the whole cyclic hardening stage, reaching 0.5 to 5%. In both cases, however, the plastic strain amplitude accommodated by twinning/detwinning, which reached 0.35-0.42% in some grains during the 1 st cycle, decreased down to less than 0.05% after 100 to 1000 cycles. (10.1016/j.msea.2021.141250)
  DOI : 10.1016/j.msea.2021.141250
• Coupled electromagnetic-thermomechanical modeling of electric motors
  
  • Hanappier Nicolas
  , 2021. Future developments of lighter, more compact and powerful motors -- driven by environmental and sustainability considerations in the transportation industry – involve higher stresses, currents and electromagnetic fields. For the components used in electric motors – especially for the ferromagnetic ones – strong couplings between mechanical, thermal and electromagnetic effects arise, which are amplified by the higher loads. They affect the machine’s performance, thus requiring a consistent multiphysics modeling for the motors’ design. Understanding and modeling these couplings has recently become an important subject of research. The work presented here proposes a coupled electromagnetic-thermomechanical continuum theory together with analytical and numerical (finite element) tools for the solutions of boundary value problems arising in electric motors.In the first part of the work, using the direct approach of continuum mechanics, based on a Eulerian (current configuration) approach, a general modeling framework coupling the electromagnetic, thermal and mechanical fields is derived from the basic principles of thermodynamics using the eddy current approximation. Although the proposed theory is general enough to account for a wide range of material behaviors, particular attention is paid to the derivation of the coupled constitutive equations for isotropic materials under small strain but arbitrary magnetization. As a first application, the theory is employed for the analytical modeling of the rotor and stator of idealized electric motor configurations for which we calculate the electric current, magnetic, stress and temperature fields. At the rotor, the different components of the stress tensor and body force vector are compared to their purely mechanical counterparts due to inertia, quantifying the significant influence of electromagnetic phenomena. At the stator, comparison with coarser models found in the electrical engineering literature is provided, quantifying the influence of the proposed model on the elastic stress and strains’ amplitudes.In the second part of the work, a variational formulation of the problem is presented based on a Lagrangian (reference configuration) approach and shown to be equivalent to the direct approach. The numerical implementation of the proposed model – via a user element in a general purpose finite element code and accounting for non-linear material behavior – is validated by comparison of the results from the analytical models of the simplified stator configuration to the numerical results for small values of the magnetic field (range of linear behavior for the magnetic field). Calculations are then performed on more complex stator configurations with a more intense magnetic field, using a non-linear magnetic response that accounts for magnetic saturation (a Langevin-type model), in order to put forward the capacities of the proposed formulation and obtain results for realistic engineering applications.
• A benchmark problem to evaluate implementational issues for three-dimensional flows of incompressible fluids subject to slip boundary conditions
  
  • Chabiniok Radomir
  • Hron Jaroslav
  • Jarolímová Alena
  • Málek Josef
  • Rajagopal Kumbakonam R
  • Rajagopal Keshava
  • Švihlová Helena
  • Tůma Karel
  Applications in Engineering Science, 2021, 6. We consider flows of an incompressible Navier-Stokes fluid in a tubular domain with Navier's slip boundary condition imposed on the impermeable wall. We focus on several implementational issues associated with this type of boundary conditions within the framework of the standard Taylor-Hood mixed finite element method and present the computational results for flows in a tubular domain of finite length with one inlet and one outlet. In particular, we present the details regarding variants of the Nitsche method concerning the incorporation of the impermeability condition on the wall. We also find that the manner in which the normal to the boundary is numerically implemented influences the nature of the computational results. As a benchmark, we set up steady flows in a tube of finite length and compare the computational results with the analytical solutions. Finally, we identify various quantities of interest, such as the dissipation, wall shear stress, vorticity, pressure drop, and provide their precise mathematical definitions. We document how well these quantities are computationally approximated in the case of the benchmark. Although the geometry of the benchmark is simple, the correct computational results require careful selection of numerical methods and surprisingly non-trivial computational resources. Our goal is to test, using the setting with a known analytical solution, a robust computational tool that would be suitable for computations on real complex geometries that have relevance to problems in engineering and medicine. The model parameters in our computations are chosen based on flows in large arteries. (10.1016/j.apples.2021.100038)
  DOI : 10.1016/j.apples.2021.100038