Publications

2023

• 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
• From domain decomposition to model reduction for Large nonlinear structures
  
  • Leturcq Bertrand
  • Le Tallec Patrick
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2023, 351 (S1), pp.1-17. The numerical simulation of multiscale and multiphysics problems requires efficient tools for spatial localization and model reduction. A general strategy combining Domain Decomposition and Nonuniform Transformation Field Analysis (NTFA) is proposed herein for the simulation of nuclear fuel assemblies at the scale of a full nuclear reactor. The model at subdomain level solves the full elastic problem but with a reduced nonlinear loading, based on simplified boundary conditions, reduced creep flow rules, projected sign preserving contact conditions, and a NTFA like reduced friction law to get the evolution of each slipping mode. With this loading reduction, the local solution can be explicitly obtained from a small set of precomputed elementary elastic solutions. The numerical tests indicate that considerable cost reduction (a factor of 50 to 1000) can be achieved while preserving engineering accuracy (10.5802/crmeca.168)
  DOI : 10.5802/crmeca.168
• Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: A macroscopic analog of thermodynamic phase transition
  
  • Gomez Michael
  • Reis Pedro
  • Audoly Basile
  Journal of the Mechanics and Physics of Solids, Elsevier, 2023, 181, pp.105420. We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so-called perversions (phase boundaries). This instability cannot be described by classical rod theory, which incorporates pre-stress through effective natural curvature and twist; these are both zero due to the mirror symmetry of the pre-stress. Using dimension reduction, we derive a one-dimensional (1D) `rod-like' model from a plate theory, which accounts for inhomogeneous pre-stress as well as finite rotations. The 1D model successfully captures the qualitative features of torsional buckling under a prescribed end-to-end displacement and rotation, including the co-existence of buckled phases possessing opposite twist, and is in good quantitative agreement with the results of numerical (finite-element) simulations and model experiments on elastomeric samples. Our model system provides a macroscopic analog of phase separation and pressure-volume-temperature state diagrams, as described by the classical thermodynamic theory of phase transitions. (10.1016/j.jmps.2023.105420)
  DOI : 10.1016/j.jmps.2023.105420
• 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
• 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.