Publications

2020

• 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
• 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
• Mathematical analysis of a penalization strategy for incompressible elastodynamics
  
  • Caforio Federica
  • Imperiale Sébastien
  Asymptotic Analysis, IOS Press, 2020. This work addresses the mathematical analysis - by means of asymptotic analysis - of a penalisation strategy for the full discretisation of elastic wave propagation problems in quasi-incompressible media that has been recently developed by the authors. We provide a convergence analysis of the solution of the continuous version of the penalised problem towards its formal limit when the penalisation parameter tends to infinity. Moreover, as a fundamental intermediate step we provide an asymptotic analysis of the convergence of solutions of quasi-incompressible problems towards solutions of purely incompressible problems when the incompressibility parameter tends to infinity. Finally, we further detail the regularity assumptions required to guarantee that the mentioned convergence holds.
• Left ventricular torsion obtained using equilibrated warping in patients with repaired Tetralogy of Fallot
  
  • Castellanos Daniel Alexander
  • Škardová Kateřina
  • Bhattaru Abhijit
  • Greil Gerald
  • Tandon Animesh
  • Dillenbeck Jeanne
  • Burkhardt Barbara
  • Hussain Tarique
  • Genet Martin
  • Chabiniok Radomir
  , 2020.
• Mathematical modelling of Acoustic Radiation Force in transient shear wave elastography in the heart
  
  • Caforio Federica
  • Imperiale Sébastien
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2020. The aim of this work is to provide a mathematical model and analysis of the excitation and the resulting shear wave propagation in Acoustic Radiation Force (ARF)-based shear wave cardiac elastography. Our approach is based on asymptotic analysis; more precisely, it consists in considering a family of problems, parametrised by a small parameter inversely proportional to the excitation frequency of the probes, the viscosity and the velocity of pressure wave propagation. We derive a simplified model for the expression of the ARF by investigating the limit behaviour of the solution when the small parameter goes to zero. By formal asymptotic analysis - an asymptotic expansion of the solution is used - and energy analysis of the nonlinear elastodynamic problem, we show that the leading- order term of the expansion is solution of the underlying, incompressible, nonlinear cardiac mechanics. Subsequently, two corrector terms are derived. The first is a fast-oscillating pressure wave generated by the probes, solution of a Helmholtz equation at every time. The second corrector term consists in an elastic field with prescribed divergence, having a function of the first corrector as a source term. This field corresponds to the shear acoustic wave induced by the ARF. We also confirm that, in cardiac mechanics, the presence of viscosity in the model is essential to derive an expression of the shear wave propagation from the ARF, and that this phenomenon is related to the nonlinearity of the partial differential equation.
• Microstructural deformation observed by Mueller polarimetry during traction assay on myocardium samples
  
  • Tueni Nicole
  • Vizet Jérémy
  • Genet Martin
  • Pierangelo Angelo
  • Allain Jean-Marc
  Scientific Reports, Nature Publishing Group, 2020, 10, pp.20531. Despite recent advances, the myocardial microstructure remains imperfectly understood. In particular, bundles of cardiomyocytes have been observed but their three-dimensional organisation remains debated and the associated mechanical consequences unknown. One of the major challenges remains to perform multiscale observations of the mechanical response of the heart wall. For this purpose, in this study, a full-field Mueller polarimetric imager (MPI) was combined, for the first time, with an in-situ traction device. The full-field MPI enables to obtain a macroscopic image of the explored tissue, while providing detailed information about its structure on a microscopic scale. Specifically it exploits the polarization of the light to determine various biophysical quantities related to the tissue scattering or anisotropy properties. Combined with a mechanical traction device, the full-field MPI allows to measure the evolution of such biophysical quantities during tissue stretch. We observe separation lines on the tissue, which are associated with a fast variation of the fiber orientation, and have the size of cardiomyocyte bundles. Thus, we hypothesize that these lines are the perimysium, the collagen layer surrounding these bundles. During the mechanical traction, we observe two mechanisms simultaneously. On one hand, the azimuth shows an affine behavior, meaning the orientation changes according to the tissue deformation, and showing coherence in the tissue. On the other hand, the separation lines appear to be resistant in shear and compression but weak against traction, with a forming of gaps in the tissue. (10.1038/s41598-020-76820-w)
  DOI : 10.1038/s41598-020-76820-w
• 3D sub-millimeter personalized estimation of cardiomyocyte orientation using dimensionality reduction
  
  • Stimm Johanna
  • Buoso Stefano
  • Genet Martin
  • Kozerke Sebastian
  • Stoeck Christian T
  , 2020.
• Plastic strain localization induced by microstructural gradient in laser cladding repaired structures
  
  • Guévenoux Camille
  • Hallais Simon
  • Balit Yanis
  • Charles Alexandre
  • Charkaluk Eric
  • Constantinescu Andrei
  Theoretical and Applied Fracture Mechanics, Elsevier, 2020, 107, pp.102520. Laser Cladding is an additive manufacturing technology well suited for the repair of complex metallic components. The repair is a two-step process: first, one removes the worn region and then, the initial geometry is reconstructed locally. The aim of this work is to study the influence of the microstructural gradient on the strain localization in repaired structures. More precisely, we perform in-situ SEM tensile tests completed by EBSD observations of the microstructure in the interface neighborhood between the base material and the repaired region. Furthermore, we monitor the evolution of the local plastic strain distribution at the grain level until failure. This is performed by Digital Image Correlation methods and superposition of grains contours and strain maps. The observations of grain size and plasticity are compared with predictions provided by a Hall-Petch model. The study emphasizes the importance of the microstructural gradient in the vicinity of reparation interface, more precisely it reveals that this gradient induce multiaxial strains and that the strain localization phenomenon is governed mainly by a grain size effect (10.1016/j.tafmec.2020.102520)
  DOI : 10.1016/j.tafmec.2020.102520
• Variational phase-field continuum model uncovers adhesive wear mechanisms in asperity junctions
  
  • Collet Sylvain
  • Molinari Jean-François
  • Brach Stella
  Journal of the Mechanics and Physics of Solids, Elsevier, 2020. Wear is well known for causing material loss in a sliding interface. Available macroscopic approaches are bound to empirical fitting parameters, which range several orders of magnitude. Major advances in tribology have recently been achieved via Molecular Dynamics, although its use is strongly limited by computational cost. Here, we propose a study of the physical processes that lead to wear at the scale of the surface roughness, where adhesive junctions are formed between the asperities on the surface of the materials. Using a brittle formulation of the variational phase-field approach to fracture, we demonstrate that the failure mechanisms of an adhesive junction can be linked to its geometry. By imposing specific couplings between the damage and the elastic energy, we further investigate the triggering processes underlying each failure mechanism. We show that a large debris formation is mostly triggered by tensile stresses while shear stresses lead to small or no particle formation. We also study groups of junctions and discuss how microcontact interactions can be favored in some geometries to form macro-particles. This leads us to propose a classification in terms of macroscopic wear rate. Although based on a continuum approach, our phase-field calculations are able to effectively capture the failure of adhesive junctions, as observed through discrete Molecular Dynamics simulations.
• 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
• 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
• 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
• 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