Publications

2020

• 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.
• Comparison of the finite strain macroscopic behavior and local damage of a soft matrix highly reinforced by spherical or polyhedral particles
  
  • de Francqueville Foucault
  • Gilormini Pierre
  • Diani Julie
  • Vandenbroucke Aude
  European Journal of Mechanics - A/Solids, Elsevier, 2020, 84, pp.1-7. Motivated by the different uniaxial responses of two actual materials filled with either sifted glass beads or sifted glass grits, the influence of the fillers shape on the finite strain behavior of highly filled composites (>50%) is examined through micromechanical finite element simulations accounting for matrix/filler debonding with a cohesive-zone model. Three-dimensional matrix cells filled with 64 monosized spherical particles are compared to cells filled with the same number of monosized polyhedra. For this purpose, an original generation process was developed to obtain periodic cells with random dispersions of non-regular polyhedra. Finite element simulations of uniaxial tensile tests on the periodic cells allow studying the influence of the fillers shape on the macroscopic behavior and on the local damage at the matrix/filler interfaces. Actually, the presence of sharp edges and apexes for polyhedral particles seems to have a second order impact compared to the cohesive-zone parameters. The damage fields demonstrate the same trends for both particles shapes. The different behaviors observed on actual composites are rather due to different adhesion properties between fillers and matrix than to the shape of particles. (10.1016/j.euromechsol.2020.104070)
  DOI : 10.1016/j.euromechsol.2020.104070
• 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
• 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.