Publications

2020

• Two families of explicit models constructed from a homogenization solution for the magnetoelastic response of MREs containing iron and ferrofluid particles
  
  • Lefèvre Victor
  • Danas Kostas
  • Lopez-Pamis Oscar
  International Journal of Non-Linear Mechanics, Elsevier, 2020, 119, pp.103362. This work puts forth two families of fully explicit continuum or phenomenological models that are constructed by approximating an analytical (but implicit) homogenization solution recently derived for the free-energy function describing the macroscopic magnetoelastic response of two classes of MREs comprised of an isotropic incompressible elastomer filled with a random isotropic distribution of: i) spherical iron particles and ii) spherical ferrofluid particles. Both families are given in terms of free-energy functions W H = W H (F, H) that depend on the deformation gradient F and the Lagrangian magnetic field H and are constructed so as to agree identically with the homogenization solution for small and large applied magnetic fields, this for arbitrary finite deformations and arbitrary volume fractions c of particles in the entire physical range c ∈ [0, 1]. The accuracy of the proposed phenomenological models is assessed inter alia via the direct comparison of their predictions with that of the homogenization solution for a boundary-value problem of both fundamental and practical significance: the magnetostriction response of a spherical MRE specimen subject to a remotely applied uniform magnetic field. (10.1016/j.ijnonlinmec.2019.103362)
  DOI : 10.1016/j.ijnonlinmec.2019.103362
• Experimental investigation and modelling of the curing behaviour of photopolymers
  
  • Rehbein T.
  • Lion A.
  • Johlitz M.
  • Constantinescu Andrei
  Polymer Testing, Elsevier, 2020, 83, pp.106356. This paper focuses on the experimental investigation and modelling of the crosslinking reaction of photopolymers used in additive manufacturing processes such as digital light processing and stereolithography. Starting with general mathematical concepts for the description of the material behaviour of polymeric materials, the importance of modelling the crosslinking reaction is emphasized. In order to characterise the crosslinking reaction experimentally, photocalorimetric measurements with varying isothermal temperature and light intensity are shown. From the exothermic heat flows measured during the crosslinking reaction, the degree of cure can be determined for each experimental scenario as a function of time. It is shown that the test temperature and light intensity have a significant influence on the crosslinking reaction. A modelling approach for the description of the crosslinking reaction incorporating temperature and light intensity is presented. Moreover, parameter identification and a comparison of the proposed model with the experiments are conducted. The indentified model has an excellent match with experimental data, resulting in a least square error smaller than 3 %. The proposed model and identification method opens up several extensions for the modelling of the material behaviour. (10.1016/j.polymertesting.2020.106356)
  DOI : 10.1016/j.polymertesting.2020.106356
• Asymptotically exact strain-gradient models for nonlinear slender elastic structures: a systematic derivation method
  
  • Lestringant Claire
  • Audoly Basile
  Journal of the Mechanics and Physics of Solids, Elsevier, 2020, pp.103730. We propose a general method for deriving one-dimensional models for nonlinear structures. It captures the contribution to the strain energy arising not only from the macroscopic elastic strain as in classical structural models, but also from the strain gradient. As an illustration, we derive one-dimensional strain-gradient models for a hyper-elastic cylinder that necks, an axisymmetric membrane that produces bulges, and a two-dimensional block of elastic material subject to bending and stretching. The method o↵ers three key advantages. First, it is nonlinear and accounts for large deformations of the cross-section, which makes it well suited for the analysis of localization in slender structures. Second, it does not require any a priori assumption on the form of the elastic solution in the cross-section, i.e., it is Ansatz-free. Thirdly, it produces one-dimensional models that are asymptotically exact when the macroscopic strain varies on a much larger length scale than the cross-section diameter. (10.1016/j.jmps.2019.103730)
  DOI : 10.1016/j.jmps.2019.103730
• Contributions à la réalisation d’une touche de piano numérique : modélisation, simulation, réalisation de prototype
  
  • Chichignoud Jérémie
  , 2020. Le travail présenté dans cette thèse représente une étape dans le projet de longs termes visant à obtenir une touche de synthétiseur muni d'un actuateur dont la fonction est de reproduire le toucher d'un piano à queue.Après une introduction présentant les problématiques du projet et l’état de l’art, nous présentons le modèle mécanique de la touche proposé par J. Lozada, puis A. Thorin, dont certains éléments ont dû être précisés et auquel plusieurs approximations et simplifications ont dû être ajoutées explicitement. Une description détaillée de la géométrie des contacts est donnée.La simulation proposée jusqu’ici était loin du temps réel en raison du choix logiciel effectué. Nous avons écrit deux programmes de simulation du modèle : l’un en matlab, à fins de prototypage et l’autre en C qui tourne en temps réel jusqu’à 6 us sur un processeur i7. Cette simulation respecte le caractère non-régulier des frottements secs dans les articulations et certains contacts unilatéraux.Les points critiques susceptibles de déstabiliser la simulation en temps réel sont discutés.L’actuateur retenu depuis longtemps dans la coopération LMS-LISA – frein à FMR – ne permettait pas de faire remonter la touche après l’action du pianiste. Nous avons donc complété le dispositif par un ensemble d’aimants permanents dont nous présentons le dimensionnement.La troisième partie du mémoire est consacrée à l’implémentation du dispositif « touche numérique ». Le choix d'un ordinateur standard comme organe de calcul et les contraintes du temps réel à une fréquence d’au moins 2 kHz ont nécessité le développement d'une communication USB spécifique pour échanger les données (mesures et commande) entre le micro-ordinateur et l’ensemble capteurs-actionneur.Nous donnons in fine les tout premiers résultats obtenus sur cet ensemble intégré. Leur analyse permet de tirer quelques conclusions relatives au développement futur du projet.
• Investigation of phase-contrast magnetic resonance imaging underestimation of turbulent flow through the aortic valve phantom: Experimental and computational study using lattice Boltzmann method
  
  • Fučík Radek
  • Galabov Radek
  • Pauš Petr
  • Eichler Pavel
  • Klinkovský Jakub
  • Straka Robert
  • Tintěra Jaroslav
  • Chabiniok Radomir
  Magnetic Resonance Materials in Physics, Biology and Medicine, Springer Verlag, 2020, 33 (5), pp.649-662. Objective: The accuracy of phase-contrast magnetic resonance imaging (PC-MRI) measurement is investigated using a computational fluid dynamics (CFD) model with the objective to determine the magnitude of the flow underestimation due to turbulence behind a narrowed valve in a phantom experiment. Materials and Methods: An acrylic stationary flow phantom is used with three insertable plates mimicking aortic valvular stenoses of varying degrees. Positive and negative horizontal fluxes are measured at equidistant slices using standard PC-MRI sequences by 1.5T and 3T systems. The CFD model is based on the 3D lattice Boltzmann method (LBM). The experimental and simulated data are compared using the Bland-Altman-derived limits of agreement. Based on the LBM results, the turbulence is quantified and confronted with the level of flow underestimation. Results: LBM gives comparable results to PC-MRI for valves up to moderate stenosis on both field strengths. The flow magnitude through a severely stenotic valve was underestimated due to signal void in the regions of turbulent flow behind the valve, consistently with the level of quantified turbulence intensity. Discussion: Flow measured by PC-MRI is affected by noise and turbulence. LBM can simulate turbulent flow efficiently and accurately, it has therefore the potential to improve clinical interpretation of PC-MRI.
• Dobutamine stress testing in patients with Fontan circulation augmented by biomechanical modeling
  
  • Ruijsink Bram
  • Zugaj Konrad
  • Wong James
  • Pushparajah Kuberan
  • Hussain Tarique
  • Moireau Philippe
  • Razavi Reza
  • Chapelle Dominique
  • Chabiniok Radomir
  PLoS ONE, Public Library of Science, 2020. Understanding (patho)physiological phenomena and mechanisms of failure in patients with Fontan circulation-a surgically established circulation for patients born with a functionally single ventricle-remains challenging due to the complex hemodynamics and high inter-patient variations in anatomy and function. In this work, we present a biomechanical model of the heart and circulation to augment the diagnostic evaluation of Fontan patients with early-stage heart failure. The proposed framework employs a reduced-order model of heart coupled with a simplified circulation including venous return, creating a closed-loop system. We deploy this framework to augment the information from data obtained during combined cardiac catheterization and magnetic resonance exams (XMR), performed at rest and during dobutamine stress in 9 children with Fontan circulation and 2 biventricular controls. We demonstrate that our modeling framework enables patient-specific investigation of myocardial stiffness, contractility at rest, contractile reserve during stress and changes in vascular resistance. Hereby, the model allows to identify key factors underlying the pathophysiological response to stress in these patients. In addition, the rapid personalization of the model to patient data and fast simulation of cardiac cycles make our framework directly applicable in a clinical workflow. We conclude that the proposed modeling framework is a valuable addition to the current clinical diagnostic XMR exam that helps to explain patient-specific stress hemodynamics and can identify potential mechanisms of failure in patients with Fontan circulation. (10.1371/journal.pone.0229015)
  DOI : 10.1371/journal.pone.0229015
• Characterization and modeling of the thermo-mechanical behavior of a Ti-6Al-4V alloy under dynamic complex loading
  
  • Ruiz de Sotto Miguel
  , 2020. During the aircraft engine certification, various components are tested against ballistic phenomena. The engine fan must accordingly resist bird strike and blade loss without compromising the whole engine thrust performance. Fan blades, and particularly their leading edge, undergo large deformation under high strain rate, non-proportional loading paths and plastic dissipation induced self-heating. Due to their high specific mechanical properties, Ti-6Al-4V titanium alloys are promising candidates for fan multi-component blade leading edge. In this work, an experimental campaign has been carried out on a cold rolled Ti-6Al-4V alloy comprising tension, compression and shear tests performed at various temperatures and (low and high) strain rates, under monotonic and alternated loading paths. Based on these results, a constitutive model has been developed accounting for the combined effects of orthotropy, strength differential, nonlinear kinematic and isotropic hardenings, strain rate hardening as well as thermal softening. Material constants have been identified using Zset software. The model has been implemented as user material (Fortran) subroutine into the commercial finite element computation code LS-DYNA. The performances of the numerical model have then been estimated by conducting numerical simulations considering a volume element under various loading paths as well as the specimens used for the experimental campaign.
• Determination of effective stress intensity factors under mixed‐mode from digital image correlation fields in presence of contact stresses and plasticity
  
  • Bonniot Thomas
  • Doquet Véronique
  • Mai Si Hai
  Strain, Wiley-Blackwell, 2020. Digital image correlation (DIC) is more and more popular to monitor fatigue crack growth and to determine the stress intensity factors. However, the posttreatment of the recorded displacement fields becomes tricky when the crack faces are not stress‐free and when crack tip plasticity becomes significant. Several posttreatment methods to locate the crack tip and measure the effective stress intensity factors in such cases are compared, using finite element method‐computed displacement fields, and then used on real DIC fields. An approach coupling DIC and finite element method is proposed to estimate the contact stresses along the crack. (10.1111/str.12332)
  DOI : 10.1111/str.12332
• Intrinsic formulations of the nonlinear Kirchhoff-Love-von Kármán plate theory
  
  • Geymonat Giuseppe
  • Krasucki Françoise
  , 2020. We use a special duality by perturbation in optimization to find two different bi-duals problems of the non-linear Kirchhoff-Love-von Kármán plate theory. The first gives exactly the intrinsic approach developed by P. G. Ciarlet, the second gives an intrinsic approach implied by a J.J. Telega complementary energy.
• Stability of Vicinal Surfaces: Beyond the Quasistatic Approximation
  
  • Guin Laurent
  • Jabbour Michel E
  • Shaabani Ardali Léopold
  • Benoit-Marechal Lucas
  • Triantafyllidis Nicolas
  Physical Review Letters, American Physical Society, 2020. We revisit the step bunching instability without recourse to the quasistatic approximation and show that the stability diagrams are significantly altered, even in the low-deposition regime where it was thought sufficient. In particular, steps are unstable against bunching for attachment-detachment limited growth. By accounting for the dynamics and chemical effects, we can explain the onset of step bunching in Si(111)−(7×7) and GaAs(001) without resort to the inverse Schwoebel barrier or step-edge diffusion. Further, the size-scaling analysis of step-bunch growth, as induced by these two combined effects, agrees with the bunching regime observed at 750 °C in Si(111)−(7×7). (10.1103/PhysRevLett.124.036101)
  DOI : 10.1103/PhysRevLett.124.036101
• Surface waves from flexural and compressional resonances of beams
  
  • Marigo Jean-Jacques
  • Pham Kim
  • Maurel Agnes
  • Guenneau Sébastien
  , 2020.
• Effective model for elastic waves propagating in a substrate supporting a dense array of plates/beams with flexural resonances
  
  • Marigo Jean-Jacques
  • Pham Kim
  • Maurel Agnès
  • Guenneau Sebastien
  , 2020. We consider the effect of an array of plates or beams over a semi-infinite elastic ground on the propagation of elastic waves hitting the interface. The plates/beams are slender bodies with fle-xural resonances at low frequencies able to perturb significantly the propagation of waves in the ground. An effective model is obtained using asymptotic analysis and homogenization techniques , which can be expressed in terms of the ground alone with effective dynamic (frequency-dependent) boundary conditions of the Robin's type. For an incident plane wave at oblique incidence, the displacement fields and the reflection coefficients are obtained in closed forms and their validity is inspected by comparison with direct numerics in a two-dimensional setting.
• Personalized Pulmonary Poromechanics
  
  • Genet Martin
  • Patte Cécile
  • Chapelle Dominique
  , 2020. Lung biomechanics has been extensively studied by physiologists, experimentally as well as theoretically , laying the ground for our current fundamental understanding of the relationship between function and mechanical behavior. However, many questions remain, notably in the intricate coupling between the multiple constituents. These fundamental questions represent real clinical challenges, as pulmonary diseases are an important health burden. Interstitial lung diseases, for instance, affect several million people globally. Idiopathic Pulmonary Fibrosis (IPF), notably, a progressive form of interstitial lung diseases where some alveolar septa get thicker and stiffer while others get completely damaged, remains poorly understood, poorly diagnosed, and poorly treated. In this presentation, I will first describe our recently developed lung poromechanical model. It lies at the organ space scale and breathing time scale, and is written in a general poromechanical mixture framework. I will also detail the specific boundary conditions imposed on the lungs themselves, modeling the effect of diaphragm-induced loading and rib cage. The second part of the presentation will deal with the personalization procedure we developed alongside the model. It allows to personalize parts of the boundary conditions and material model from biomedical images, after processing. I will notably insist on the inverse problem of finding the unloaded configuration associated to the loaded configuration observed in vivo, and associated issues. Then I will show how regional mechanical parameters can be estimated in diseased lungs, illustrating how this model could be used as a diagnosis tool in the clinic.
• A constitutive model for a rate and temperature dependent, plastically anisotropic titanium alloy
  
  • Ruiz de Sotto Miguel
  • Longère Patrice
  • Doquet Véronique
  • Papasidero Jessica
  , 2020. This study focuses on the design of fan blades regarding impact loading resulting mostly from bird strike or engine fan blade loss and involving large deformation, high rate of deformation, non-proportional loading paths, plastic dissipation induced heating and potential damage and fracture. Due to their high strength-to-weight ratio and good toughness, Ti-6Al-4V titanium alloys are promising candidates for the leading edge of multi-component fan blades. To get a reliable prediction of the resistance of the whole engine structure, an extensive experimental campaign has been carried out and a constitutive model has been developed for a grade of Ti-6Al-4V titanium alloy provided in the form of cold rolled plates. The thermo-mechanical characterization, consisted of tension, compression and shear tests at various temperatures, (quasi static and dynamic) strain rates and (monotonic and alternate) loading paths, has evidenced a strong temperature and rate dependence as well as an orthotropic behavior with a significant tension/compression dissymmetry and a combination of isotropic and kinematic strain hardening. A constitutive model has been accordingly developed accounting for the combined effect of nonlinear, isotropic and kinematic strain hardening, strain rate hardening, tension/compression dissymmetry and machining direction. For that purpose, orthotropic plasticity models have been extended within a rate-dependent and isotropic vs. kinematic hardening formulation. The identification of the constitutive model constants has been conducted by means of the commercial software Zset. The constitutive model has then been implemented as a user material subroutine into the commercial finite element computation code LS-DYNA. Numerical simulations have been conducted considering some basic cases involving representative volume elements as well as structures such as the specimens used for the experimental campaign.
• Effect of Strains on the Dark Current-Voltage Characteristic of Silicon Heterojunction Solar Cells
  
  • Guin Laurent
  • Roca I Cabarrocas Pere
  • Jabbour Michel E
  • Triantafyllidis Nicolas
  Solar Energy, Elsevier, 2020. Anisotropic mechanical strain as low as 0.1% modifies the electronic response of crystalline semiconductor- based devices and in particular affects the performance of solar cells. We measure the dark current-voltage characteristic of silicon heterojunction solar cells under different levels of tensile uniaxial stress and observe a reversible change of the j-V curve with applied strain. Using a two-exponential description of the j-V char- acteristic to fit our experimental data, we obtain the strain dependence of the diffusion saturation current and find a decrease of about 3% for a tensile strain level of 6.7 × 10 4 . We compare these experiments to a theoretical model that accounts for the effect of strain on the band energy levels, densities of states and mobilities of carriers. The theoretical estimation of the change in saturation current is found to be in reasonable agreement with experimental results. (10.1016/j.solener.2019.12.037)
  DOI : 10.1016/j.solener.2019.12.037
• Digital image correlation for microstructural analysis of deformation pattern in additively manufactured 316L thin walls
  
  • Balit Yanis
  • Charkaluk Eric
  • Constantinescu Andrei
  Additive Manufacturing, Elsevier, 2020, 31, pp.100862. In additive manufacturing, the process parameters have a direct impact on the microstructure of the material and consequently on the mechanical properties of the manufactured parts. The purpose of this paper is to explore this relation by characterizing the local microstructural response via in situ tensile test under a scanning electron microscope (SEM) combined with high resolution digital image correlation (HR-DIC) and electron backscat-ter diffraction (EBSD) maps. The specimens under scrutiny were extracted from bidirectionally-printed single-track thickness 316L stainless steel walls built by directed energy deposition. The morphologic and crystallographic textures of the grains were characterized by statistical analysis and associated with the particular heat flow pattern of the process. Grains were sorted according to their size into large columnar grains located within the printed layer and small equiaxed grains located at the interfaces between successive layers. In situ tensile experiments were performed with a loading direction either perpendicular or along the printing direction and exhibit different mechanisms of deformation. A statistical analysis of the average deformation per grain indicates that for a tensile loading along the building direction, small grains deform less than the large ones. In addition, HR-DIC combined with EBSD maps showed strain localization situated at the interface between layers in the absence of small grains either individual or in clusters. For tensile loads along the printing direction, the strain localization was present 1 Additive Manufacturing 31 (2020) 100862 https://doi. in several particular large grains. These observations permit to justify the differences in yield and ultimate strength noticed during macroscopic tensile tests for both configurations. Moreover, they indicate that an optimization of the process parameters could trigger the control of microstructure and consequently the macroscopic mechanical behavior. (10.1016/j.addma.2019.100862)
  DOI : 10.1016/j.addma.2019.100862
• Foreword
  
  • Diani J.
  • Castelnau O
  • Chinesta Francisco
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2020, 348, pp.781-783. La mécanique des matériaux, qu’il s’agisse d’alliages métalliques, de polymères, de composites, ou encore de minéraux, est un domaine de recherche vaste s’appuyant aussi bien sur la physique, la chimie, les mathématiques, les techniques numériques, que les sciences expérimentales. Elle a la particularité de traverser les échelles de l’atome au milieu continu macroscopique.En particulier, la prise en compte des mécanismes élémentaires de déformation aux échelles pertinentes permet la construction de modèles de comportement robustes, i.e. qui soient capables non seulement de reproduire fidèlement les observations mais aussi de prédire le comportement mécanique dans des conditions inexplorées ou inexplorables expérimentalement. (10.5802/crmeca.65)
  DOI : 10.5802/crmeca.65
• Maximum admissible pressure in salt caverns used for brine production and hydrocarbon storage
  
  • Berest Pierre
  • Brouard Benoît
  • Karimi-Jafari Mehdi
  • Réveillère Arnaud
  Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles, Institut Français du Pétrole (IFP), 2020, 75, pp.76. Tightness is a fundamental prerequisite to any underground storage. In storage salt caverns, a safe maximum admissible pressure must be selected to avoid product loss. The tensile strength of salt is small, and cavern pressure must be kept lower than geostatic pressure or, more precisely, lower than the least compressive stress at the cavern wall. The vertical stress can be assessed through density logs. The redistribution of stresses in the rock mass, due to the visco-plastic nature of rock salt, must be taken into account. A couple of cases in which a hydraulic connection between one cavern and another cavern, or between a cavern and the edge of a salt dome, are known. These connections originated in geological anomalies rather than in the creation of a fracture. There exists a pressure threshold, lower than the geostatic pressure, for which micro-fracturing and an increase in salt permeability occur, vindicating the position that a safety margin is needed when selecting the maximum pressure. Well tightness is important as well; it depends on several factors, among which are the quality of the cement, and the maximum fluid pressure in the cavern and along the access well. A tightness test is mandatory. The Nitrogen Leak Test is the most common such test. A review of selected gas-storage sites shows that, in most cases, the maximum admissible gradient at the casing shoe is 0.018 MPa/m (0.8 psi/ft), and up to 0.019 MPa/m (0.85 psi/ft) in some American states, values that are consistent with the considerations listed above. (10.2516/ogst/2020068)
  DOI : 10.2516/ogst/2020068
• Analysis of boundary layer effects due to usual boundary conditions or geometrical defects in elastic plates under bending: an improvement of the Love-Kirchhoff model
  
  • León Baldelli Andrés Alessandro
  • Marigo Jean-Jacques
  • Pideri Catherine
  Journal of Elasticity, Springer Verlag, 2020. We propose a model of flexural elastic plates accounting for boundary layer effects due to the most usual boundary conditions or to geometrical defects, constructed via matched asymptotic expansions. In particular, considering a rectangular plate clamped at two opposite edges while the other two are free, we derive the effective boundary conditions or effective transmission conditions that the two first terms of the outer expansion must satisfy. The new boundary value problems thus obtained are studied and compared with the classical Love-Kirchhoff plate model. Two examples of application illustrate the results. (10.1007/s10659-020-09804-6)
  DOI : 10.1007/s10659-020-09804-6
• Relationship between local damage and macroscopic response of soft materials highly reinforced by monodispersed particles
  
  • de Francqueville Foucault
  • Gilormini Pierre
  • Diani Julie
  • Vandenbroucke Aude
  Mechanics of Materials, Elsevier, 2020, 146, pp.1-9. A rubberlike matrix highly filled with spherical micrometric glass beads is submitted to uniaxial tension tests until break. X-ray tomography imaging performed on the material while submitted to uniaxial tension reveals early debonding at the matrix/filler interfaces at the poles of the particles followed by void coalescence creating damage localization. The latter causes a downturn of the macroscopic stress-strain response. These phenomena are analyzed further with three-dimensional finite element simulations, where 64 spherical beads are distributed randomly in a periodic cell. A simple version of the Tvergaard-Hutchinson cohesive-zone model allows to reproduce all the experimental trends well. The effects of the three parameters involved are analyzed, and three different types of macroscopic behaviors are observed corresponding to three different microstructure damages. The value of the initial stiffness of the interface, limited by numerical convergence, has little effect on how the local damage evolves but has a significant impact on the overall macroscopic stress values. The local damage is strongly dependent on the critical strength and the separation failure displacement, and the adhesion energy may be considered as a resulting parameter of the two previous ones. The interfacial critical strength appears to have a significant impact on the damage initiation, either spread across the structure for low values, or localized for high values. Increasing the interface separation failure displacement delays the possible loss of adhesion to a higher strain and preserves the integrity of the composite material. (10.1016/j.mechmat.2020.103408)
  DOI : 10.1016/j.mechmat.2020.103408
• Fast simulation of grain growth based on Orientated Tessellation Updating Method
  
  • Weisz-Patrault Daniel
  • Sakout Sofia
  • Ehrlacher Alain
  Mechanics & Industry, EDP Sciences, 2020, 21 (5), pp.513. This work is part of a more general idea consisting in developing a macroscopic model of grain growth whose state variables contain for each material point the statistical descriptors of the microstructure (e.g., disorientation, grain size and shape distributions). The strategy is to determine macroscopic free energy and dissipation potentials on the basis of a large number of computations at the scale of the polycrystal. The aim is to determine enriched macroscopic evolution laws. For sake of simplicity, this contribution only deals with grain growth of a single phased metal without diffusion or segregation of alloying elements. In order to test this upscaling strategy it is necessary to establish a simulation tool at the scale of the polycrystal. It should be sufficiently simple and fast to enable a large number of simulations of various microstructures, even if it leads to neglect some phenomena occurring at this scale. Usual grain growth models relying on mobile finite element modeling, level set functions, phase field or molecular dynamics are too computationally costly to be used within the proposed framework. Therefore, this paper focuses on the development of a “toy” model. Tessellation techniques are usually used to approximate polycrystalline microstructures. Therefore, one can approximate the real evolution of the microstructure as a succession of tessellation approximations. It then becomes quite natural to attempt to establish the evolution law of the microstructure directly on the parameters defining the tessellation. The obtained model is very light in terms of computational cost and enables to compute a large number of evolutions within the framework of the proposed statistical upscaling method. (10.1051/meca/2020041)
  DOI : 10.1051/meca/2020041
• A continuum model for slip transfer at grain boundaries
  
  • Fressengeas Claude
  • Upadhyay Manas V
  Advanced Modeling and Simulation in Engineering Sciences, Springer, 2020. Using a continuous representation of dislocations in elastoplastic polycrystals, we investigate slip transfer at grain boundaries by assessing the compatibility of the slip system shear rates with tangential continuity of the plastic distortion rate tensor at these interfaces. Fulfillment of this tangential continuity condition is needed for consistency of the continuous description of dislocations in polycrystals. We show that, in f.c.c. materials at moderate temperatures, this condition unequivocally translates into constraints on the slip rates on both sides of grain boundaries. Appended to the elastoplastic boundary value problem, it allows a complete determination of the slip system shear rates. An algorithm enabling the implementation of compatible slip transfer in both the finite element methods and the spectral methods based on Fast Fourier Transforms is provided in both standard crystal plasticity and the mechanics of dislocations fields. (10.1186/s40323-020-00145-6)
  DOI : 10.1186/s40323-020-00145-6
• On the failure of classic elasticity in predicting elastic wave propagation in gyroid lattices for very long wavelengths
  
  • Rosi Giuseppe
  • Auffray Nicolas
  • Combescure Christelle
  Symmetry, MDPI, 2020, 12 (8), pp.1243. In this work we investigate the properties of elastic waves propagating in gyroid lattices. First, we rigorously characterize the lattice from the point of view of crystallography. Second, we use Bloch-Floquet analysis to compute the dispersion relations for elastic waves. The results for very long wavelengths are then compared to those given by classic elasticity for a cubic material. A discrepancy is found in terms of the polarization of waves and it is related to the noncentrosymmetry of the gyroid. The gyroid lattice results to be acoustically active, meaning that transverse waves exhibit a circular polarization when they propagate along an axis of rotational symmetry. This phenomenon is present even for very long wavelengths and it is not captured by classic elasticity. (10.3390/sym12081243)
  DOI : 10.3390/sym12081243
• Effects of plasticity on the anisotropy of the effective fracture toughness
  
  • Brach Stella
  International Journal of Fracture, Springer Verlag, 2020. This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the crack propagates throughout the material and the evolution of the effective toughness as a function of the layer angle. We first study three idealized situations, where only one property among fracture toughness, Young's modulus and yield strength is heterogeneous whereas the others are uniform. We observe that in the case of toughness and strength heterogeneity, the material exhibits anomalous isotropy: the effective toughness is equal to the largest of the point-wise values for any layer angle except when the layers are parallel to the macroscopic direction of propagation. As the layer angle decreases, the crack propagates along the brittle-to-tough interfaces, whereas it goes straight when the layers have different yield strength but uniform toughness. We find that smooth deflections in the crack path do not induce any overall toughening and that the effective toughness is not proportional to either the cumulated fracture energy or the cumulated plastic work. In the case of elastic heterogeneity, the material is anisotropic in the sense of the effective toughness, as the latter varies as a function of the layer angle. Four toughening mechanisms are active: stress fluctuations, crack renucleation, plastic dissipation and plastic blunting. Finally, we consider a layered medium comprised of compliant-tough-weak and stiff-brittle-strong phases, as it is the case for many structural composites. We observe a transition from an interface-dominated to a plasticity-dominated failure regime, as the phase constituents become more ductile. The material is anisotropic in the sense of the effective toughness.
• Effective resonant model and simulations in the time-domain of wave scattering from a periodic row of highly-contrasted inclusions
  
  • Touboul Marie
  • Pham Kim
  • Maurel Agnès
  • Marigo Jean-Jacques
  • Lombard Bruno
  • Bellis Cédric
  Journal of Elasticity, Springer Verlag, 2020, 142 (1), pp.53-82. The time-domain propagation of scalar waves across a periodic row of inclusions is considered in 2D. As the typical wavelength within the background medium is assumed to be much larger than the spacing between inclusions and the row width, the physical configuration considered is in the low-frequency homogenization regime. Furthermore, a high contrast between one of the constitutive moduli of the inclusions and of the background medium is also assumed. So the wavelength within the inclusions is of the order of their typical size, which can further induce local resonances within the microstructure. In Pham et al. (2017), two-scale homogenization techniques and matched-asymptotic expansions have been employed to derive, in the harmonic regime, effective jump conditions on an equivalent interface. This homogenized model is frequency-dependent due to the resonant behavior of the inclusions. In this context, the present article aims at investigating, directly in the time-domain, the scattering of waves by such a periodic row of resonant scatterers. Its effective behavior is first derived in the time-domain and some energy properties of the resulting homogenized model are analyzed. Time-domain numerical simulations are then performed to illustrate the main features of the effective interface model obtained and to assess its relevance in comparison with full-field simulations.