Publications

2023

• Discrete-time formulations as time discretization strategies in data assimilation
  
  • Moireau Philippe
  , 2023, 2, pp.297-339. Data assimilation combines control theory and scientific computing to propose a set of methods for coupling dynamic models and data sequences for estimation and prediction in all engineering domains. Data assimilation naturally raises the question of how the developed control and optimization methods interact with the discretization of the underlying physical models, in particular their temporal discretization. We would like to present here some of the best known techniques developed for discrete-time models, which are essentially based on a mechanism involving model prediction on the one hand and data correction on the other. We show that they can be considered as specific discretizations of the data assimilation strategies proposed for continuous-time models in the sense of a discretization-and-then-control approach. This paradigm justifies the stability of these prediction-correction schemes, paving the way for convergence properties and justifying their popularity in practice. (10.1016/bs.hna.2022.11.005)
  DOI : 10.1016/bs.hna.2022.11.005
• Reduced left ventricular dynamics modeling based on a cylindrical assumption
  
  • Genet Martin
  • Diaz Jérôme
  • Chapelle Dominique
  • Moireau Philippe
  International Journal for Numerical Methods in Biomedical Engineering, John Wiley and Sons, 2023. Biomechanical modeling and simulation is expected to play a significant role in the development of the next generation tools in many fields of medicine. However, full-fledged finite element models of complex organs such as the heart can be computationally very expensive, thus limiting their practical usability. Therefore, reduced models are much valuable to be used, e.g., for pre-calibration of full-fledged models, fast predictions, real-time applications, etc.. In this work, focused on the left ventricle, we develop a reduced model by defining reduced geometry & kinematics while keeping general motion and behavior laws, allowing to derive a reduced model where all variables & parameters have a strong physical meaning. More specifically, we propose a reduced ventricular model based on cylindrical geometry & kinematics, which allows to describe the myofiber orientation through the ventricular wall and to represent contraction patterns such as ventricular twist, two important features of ventricular mechanics. Our model is based on the original cylindrical model of [Guccione, McCulloch, & Waldman 1991; Guccione, Waldman, & McCulloch 1993], albeit with multiple differences: we propose a fully dynamical formulation, integrated into an open-loop lumped circulation model, and based on a material behavior that incorporates a fine description of contraction mechanisms; moreover, the issue of the cylinder closure has been completely reformulated; our numerical approach is novel as well, with consistent spatial (finite element) and time discretizations. Finally, we analyse the sensitivity of the model response to various numerical and physical parameters, and study its physiological response. (10.1002/cnm.3711)
  DOI : 10.1002/cnm.3711
• PeakForce AFM Analysis Enhanced with Model Reduction Techniques
  
  • Chang Xuyang
  • Hallais Simon
  • Danas Kostas
  • Roux Stéphane
  Sensors, MDPI, 2023, 23 (10), pp.4730. PeakForce quantitative nanomechanical AFM mode (PF-QNM) is a popular AFM technique designed to measure multiple mechanical features (e.g., adhesion, apparent modulus, etc.) simultaneously at the exact same spatial coordinates with a robust scanning frequency. This paper proposes compressing the initial high-dimensional dataset obtained from the PeakForce AFM mode into a subset of much lower dimensionality by a sequence of proper orthogonal decomposition (POD) reduction and subsequent machine learning on the low-dimensionality data. A substantial reduction in user dependency and subjectivity of the extracted results is obtained. The underlying parameters, or "state variables", governing the mechanical response can be easily extracted from the latter using various machine learning techniques. Two samples are investigated to illustrate the proposed procedure (i) a polystyrene film with low-density polyethylene nano-pods and (ii) a PDMS film with carbon-iron particles. The heterogeneity of material, as well as the sharp variation in topography, make the segmentation challenging. Nonetheless, the underlying parameters describing the mechanical response naturally offer a compact representation allowing for a more straightforward interpretation of the high-dimensional force-indentation data in terms of the nature (and proportion) of phases, interfaces, or topography. Finally, those techniques come with a low processing time cost and do not require a prior mechanical model. (10.3390/s23104730)
  DOI : 10.3390/s23104730
• High-resolution reciprocal space mapping reveals dislocation structure evolution during 3D printing
  
  • Gaudez Steve
  • Abdesselam Kouider Abdellah
  • Gharbi Hakim
  • Hegedüs Zoltan
  • Lienert Ulrich
  • Pantleon Wolfgang
  • Upadhyay Manas Vijay
  Additive Manufacturing, Elsevier, 2023, 71, pp.103602. Dislocation structures are ubiquitous in any 3D printed alloy and they play a primary role in determining the mechanical response of an alloy. While it is understood that these structures form due to rapid solidification during 3D printing, there is no consensus on whether they evolve due to the subsequent solid-state thermal cycling that occurs with further addition of layers. In order to design alloy microstructures with desired mechanical responses, it is crucial to first answer this outstanding question. To that end, a novel experiment has been conducted by employing high resolution reciprocal space mapping, a synchrotron-based X-ray diffraction technique, in situ during 3D printing of an austenitic stainless steel. It reveals that dislocation structures formed during rapid solidification undergo significant evolution during subsequent solid-state thermal cycling, in particular during addition of the first few (up to 5) layers above the layer of interest. (10.1016/j.addma.2023.103602)
  DOI : 10.1016/j.addma.2023.103602
• An energy approach to asymptotic, higher-order, linear homogenization
  
  • Audoly Basile
  • Lestringant Claire
  Journal of Theoretical, Computational and Applied Mechanics, INRIA, 2023. A higher-order homogenization method for linear elastic structures is proposed. While most existing approaches to homogenization start from the equations of equilibrium, the proposed one works at the energy level. We start from an energy functional depending on microscopic degrees of freedom on the one hand and on macroscopic variables on the other hand; the homogenized energy functional is derived by relaxing the microscopic degrees of freedom and applying a formal two-scale expansion. This method delivers the energy functional of the homogenized model directly, including boundary terms that have not been discussed in previous work. Our method is formulated in a generic setting which makes it applicable to a variety of geometries in dimension 1, 2 or 3, and without any particular assumption on material symmetry. An implementation using a symbolic calculation language is proposed and it is distributed as an open-source library. Simple illustrations to elastic trusses having pre-stress or graded elastic properties are presented. The approach is presented in the context of discrete elastic structures and the connection with previous work on the higher-order homogenization of period continua is discussed. (10.46298/jtcam.11414)
  DOI : 10.46298/jtcam.11414
• Gold metallization of hybrid organic-inorganic polymer microstructures 3D printed by two-photon polymerization
  
  • Bretosh Kateryna
  • Hallais Simon
  • Chevalier-Cesar Clotaire
  • Zucchi Gaël
  • Bodelot Laurence
  Surfaces and Interfaces, Elsevier, 2023, 39, pp.102895. Two-photon polymerization is a femtosecond laser-based technique enabling printing of three-dimensional structures down to submicron resolution within photocurable polymers. Rendering the dielectric 3D printed structures conductive can be of great benefit for various applications in domains such as energy, photonics, or multifunctional devices. In this work, the microstructures of interest are made of a silicon-zirconium hybrid organic-inorganic polymer exhibiting low shrinkage during development. A simple and efficient metallization method by electroless plating is investigated to deposit a gold layer on the surface of the printed microstructures. The influence of the method parameters on the quality and properties of the deposited layer is studied. Among these parameters, the surface modification agent concentration and step duration, as well as the seeding solution concentration, must be adapted to the specific case of the considered hybrid microstructures. The concentration of metal ions in the plating bath is the most influential parameter on the morphology of the deposited gold layers. In particular, higher concentrations lead to smooth and continuous layers with electrical conductivities higher than half that of bulk gold. Finally, the deposited layers are shown to coat 3D printed microstructures of arbitrary shapes, thus confirming the conformality of the method at the micrometric scale. (10.1016/j.surfin.2023.102895)
  DOI : 10.1016/j.surfin.2023.102895
• General guidelines for the performance of viscoelastic property identification in elastography: A Monte‐Carlo analysis from a closed‐form solution
  
  • van Houten Elijah
  • Geymonat Giuseppe
  • Krasucki Françoise
  • Wattrisse Bertrand
  International Journal for Numerical Methods in Biomedical Engineering, John Wiley and Sons, 2023, 39 (8), pp.e3741. Identification of the mechanical properties of a viscoelastic material depends on characteristics of the observed motion field within the object in question. For certain physical and experimental configurations and certain resolutions and variance within the measurement data, the viscoelastic properties of an object may become non‐identifiable. Elastographic imaging methods seek to provide maps of these viscoelastic properties based on displacement data measured by traditional imaging techniques, such as magnetic resonance and ultrasound . Here, 1D analytic solutions of the viscoelastic wave equation are used to generate displacement fields over wave conditions representative of diverse time‐harmonic elastography applications. These solutions are tested through the minimization of a least squares objective function suitable for framing the elastography inverse calculation. Analysis shows that the damping ratio and the ratio of the viscoelastic wavelength to the size of the domain play critical roles in the form of this least squares objective function. In addition, it can be shown analytically that this objective function will contain local minima, which hinder discovery of the global minima via gradient descent methods. (10.1002/cnm.3741)
  DOI : 10.1002/cnm.3741
• Finite element implementation of the thermal field dislocation mechanics model: study of temperature evolution due to dislocation activity
  
  • Lima-Chaves Gabriel Dante
  • Upadhyay Manas V
  , 2023. The fully coupled small deformation formulation of the thermal field dislocation mechanics model (Upadhyay (2020)) is numerically implemented using the finite element method. The implementation consists of solving a first-order div-curl system to obtain an incompatible plastic distortion from a prescribed polar dislocation density along with three governing partial differential equations (PDE): the dislocation transport equation (a first-order hyperbolic PDE), the static equilibrium equation (an elliptic PDE), and the temperature evolution equation (a parabolic PDE). A combination of continuous Galerkin (for the elliptic and parabolic PDEs) and discontinuous Galerkin (for the hyperbolic PDE) space discretizations and Runge-Kutta time discretizations are used to implement these equations in a staggered algorithm and obtain stable solutions at (quasi-)optimal convergence rates. The implementation is validated by comparing the simulation-predicted temperature evolution of a moving edge dislocation with an analytical solution. Next, the contribution of plastic dissipation and thermoelastic effect to the temperature evolution during the motion of an edge and a screw dislocation, annihilation of two edge dislocations and expansion of a dislocation loop are studied in detail. In the case of a moving edge dislocation, contrary to existing literature, the thermoelastic effect is demonstrated to have a more significant contribution to temperature evolution than plastic dissipation for the studied traction boundary condition and dislocation velocity expression. In the dislocation loop expansion case, the role of free surfaces on temperature evolution is highlighted. As the loop approaches the free surfaces, plastic dissipation is found to have an increasing contribution to temperature evolution due to the growing impact of image stresses.
• Profiling oocytes with neural networks from images and mechanical data
  
  • Lamont Samuel
  • Fropier Juliette
  • Abadie Joël
  • Piat Emmanuel
  • Constantinescu Andrei
  • Vernerey Franck J
  Journal of the mechanical behavior of biomedical materials, Elsevier, 2023, 138. The success rate of assisted reproductive technologies could be greatly improved by selectively choosing egg cells (oocytes) with the greatest chance of fertilization. The goal of mechanical profiling is, thus, to improve predictive oocyte selection by isolating the mechanical properties of oocytes and correlating them to their reproductive potential. The restrictions on experimental platforms, however – including minimal invasiveness and practicality in laboratory implementation – greatly limits the data that can be acquired from a single oocyte. In this study, we perform indentation studies on human oocytes and characterize the mechanical properties of the zona pellucida, the outer layer of the oocyte. We obtain excellent fitting with our physical model when indenting with a flat surface and clearly illustrate localized shear-thinning behavior of the zona pellucida, which has not been previously reported. We conclude by outlining a promising methodology for isolating the mechanical properties of the cytoplasm using neural networks and optical images taken during indentation. (10.1016/j.jmbbm.2022.105640)
  DOI : 10.1016/j.jmbbm.2022.105640
• Numerical analysis of an incompressible soft material poromechanics model using T-coercivity
  
  • Barré Mathieu
  • Grandmont Céline
  • Moireau Philippe
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2023, 351 (S1), pp.1-36. This article is devoted to the numerical analysis of the full discretization of a generalized poromechanical model resulting from the linearization of an initial model fitted to soft tissue perfusion. Our strategy here is based on the use of energy-based estimates and T-coercivity methods, so that the numerical analysis benefits from the essential tools used in the existence analysis of the continuous-time and continuous-space formulation. In particular, our T-coercivity strategy allows us to obtain the necessary inf-sup condition for the global system from the inf-sup condition restricted to a subsystem having the same structure as the Stokes problem. This allows us to prove that any finite element pair adapted to the Stokes problem is also suitable for this global poromechanical model regardless of porosity and permeability, generalizing previous results from the literature studying this model. (10.5802/crmeca.194)
  DOI : 10.5802/crmeca.194