Publications

2019

• Dispositif cardiaque
  
  • Chapelle Dominique
  • Moireau Philippe
  • Pernot Mathieu
  • Tanter Mickael
  , 2019.
• Mathematical and numerical study of transient wave scattering by obstacles with the Arlequin Method
  
  • Albella Martínez Jorge
  • Ben Dhia Hachmi
  • Imperiale Sébastien
  • Rodríguez Jerónimo
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2019. In this work we extend the Arlequin method to overlapping domain decomposition technique for transient wave equation scattering by obstacles. The main contribution of this work is to construct and analyze from the continuous level up to the fully discrete level some variants of the Arlequin method. The constructed discretizations allow to solve wave propagation problems while using non-conforming and overlapping meshes for the background propagating medium and the surrounding of the obstacle respectively. Hence we obtain a flexible and stable method in terms of the space discretization-an inf-sup condition is proven-while the stability of the time discretization is ensured by energy identities. (10.1137/19M1263959)
  DOI : 10.1137/19M1263959
• Numerical analysis for an energy-stable total discretization of a poromechanics model with inf-sup stability
  
  • Burtschell Bruno
  • Moireau Philippe
  • Chapelle Dominique
  Acta Mathematicae Applicatae Sinica, Springer Verlag, 2019, 35 (1), pp.28-53. We consider a previously proposed general nonlinear poromechanical formulation, and we derive a linearized version of this model. For this linearized model, we obtain an existence result and we propose a complete discretization strategy - in time and space - with a special concern for issues associated with incompressible or nearly-incompressible behavior. We provide a detailed mathematical analysis of this strategy, the main result being an error estimate uniform with respect to the compressibility parameter. We then illustrate our approach with detailed simulation results and we numerically investigate the importance of the assumptions made in the analysis, including the fulfillment of specific inf-sup conditions. (10.1007/s10255-019-0799-5)
  DOI : 10.1007/s10255-019-0799-5
• Very Slow Creep Tests on Salt Samples
  
  • Bérest Pierre
  • Gharbi Hakim
  • Brouard Benoit
  • Brückner Dieter
  • Devries Kerry
  • Hévin Grégoire
  • Hofer Gerd
  • Spiers Christopher
  • Urai Janos
  Rock Mechanics and Rock Engineering, Springer Verlag, 2019, 52 (9), pp.2917-2934. The objective of this paper is to assess the creep law of natural salt in a small deviatoric stress range. In this range, creep is suspected to be much faster than what is predicted by most constitutive laws used in the cavern and mining industries. Five 2-year, multistage creep tests were performed with creep-testing devices set in a gallery of the Altaussee mine in Austria to take advantage of the very stable temperature and humidity conditions in this salt mine. Each stage was 8-month long. Dead loads were applied, and vertical displacements were measured through gages that had a resolution of 12.5 nm. Loading steps were 0.2, 0.4, and 0.6 MPa, which are much smaller than the loads that are usually applied during creep tests (5–20 MPa). Five salt samples were used: two samples were cored from the Avery Island salt mine in Louisiana, United States; two samples were cored from the Gorleben salt mine in Germany; and one sample was cored from a deep borehole at Hauterives in Drôme, France. During these tests, transient creep is relatively long (6–10 months). Measured steady-state strain rates ( = 10−13–10−12 s−1) are much faster (by 7–8 orders of magnitude) than those extrapolated from relatively high-stress tests (σ = 5–20 MPa). When compared to n = 5 within the high-stress domain for Gorleben and Avery Island salts, a power-law stress exponent within the low-stress domain appears to be close to n = 1. These results suggest that the pressure solution may be the dominant deformation mechanism in the steady-state regime reached by the tested samples and will have important consequences for the computation of caverns or mines behavior. This project was funded by the Solution-Mining Research Institute. (10.1007/s00603-019-01778-9)
  DOI : 10.1007/s00603-019-01778-9
• One-dimensional modeling of necking in rate-dependent materials
  
  • Audoly Basile
  • Hutchinson John
  Journal of the Mechanics and Physics of Solids, Elsevier, 2019, 123, pp.149. This paper presents an asymptotically rigorous one-dimensional analytical formulation capable of accurately capturing the stress and strain distributions that develop within the evolving neck of bars and sheets of rate-dependent materials stretched in tension. The work is an extension of an earlier study by the authors on necking instabilities in rate-independent materials. The one-dimensional model accounts for the gradients of the stress and strain that develop as the necking instability grows. Material strain-rate dependence has a significant influence on the strain that can be imposed on a bar or sheet before necking becomes pronounced. The formulation in this paper enables a quantitative assessment of the interplay in necking retardation due to rate-dependence and that due to the development of hydrostatic tension in the neck. The connection with a much simpler long-wavelength approximation which does not account for curvature induced hydrostatic tension in the neck is also emphasized and extended. (10.1016/j.jmps.2018.08.005)
  DOI : 10.1016/j.jmps.2018.08.005
• Multiscale characterization of skin mechanics through in situ imaging
  
  • Allain Jean-Marc
  • Lynch Barbara
  • Schanne-Klein Marie-Claire
  , 2019, 22, pp.265-280. The complex mechanical properties of skin have been studied intensively over the past decades. They are intrinsically linked to the structure of the skin at several length scales, from the macroscopic layers (epidermis, dermis and hypodermis) down to the microstructural organization at the molecular level. Understanding the link between this microscopic organization and the mechanical properties is of significant interest in the cosmetic and medical fields. Nevertheless, it only recently became possible to directly visualize the skin’s microstructure during mechanical assays, carried out on the whole tissue or on isolated layers. These recent observations have provided novel information on the role of structural components of the skin in its mechanical properties, mainly the collagen fibers in the dermis, while the contribution of others, such as elastin fibers, remains elusive. In this chapter we present current methods used to observe skin’s microstructure during a mechanical assay, along with their strengths and limitations, and we review the unique information they provide on the link between structure and function of the skin. (10.1007/978-3-030-13279-8_8)
  DOI : 10.1007/978-3-030-13279-8_8
• An Evolving Switching Surface Model for Ferromagnetic Hysteresis
  
  • Mukherjee D.
  • Danas Kostas
  Journal of Applied Physics, American Institute of Physics, 2019, 125 (3), pp.033902. We propose a thermodynamically consistent rate-independent three-dimensional model of magnetic hysteresis in terms of energetic and dissipation potentials making use of a relatively small number of model parameters that is capable of being implemented in a general incremental numerical setting. The dissipation process occurring during magnetization/demagnetization is described by a power-law potential, which leads to rate-independence at a certain limit of the rate-dependent exponent. The incorporation of isotropic hardening in the model enables us to describe phenomenologically at the macroscopic scale both nucleation and pinning type constitutive responses. We further model the symmetric and asymmetric minor loops by employing the idea of a bounding surface, which was originally introduced in the context of mechanical plasticity. Our model shows a very good agreement with experiments for spark plasma sintered NdFeB magnets, where nucleation is found to be the primary mechanism of coercivity. We also use our model to probe experiments for melt-spun NdFeB ribbons and powders, where both nucleation and pinning mechanisms are experimentally found to be significant. Moreover, we correlate the proposed model parameters with the underlying mechanisms for coercivity. Finally, we probe the predictive capability of the proposed model by first fitting an experimental minor loop, and then use it to successfully predict the remaining minor loops, obtained from that experiment. We also construct a FORC diagram for the floppy disc material and compare it with the corresponding experimental data. (10.1063/1.5051483)
  DOI : 10.1063/1.5051483
• Ultrafine versus coarse grained Al 5083 alloys: From low-cycle to very-high-cycle fatigue
  
  • Li Meng
  • Goyal Anchal
  • Doquet Véronique
  • Ranc Nicolas
  • Couzinié Jean-Philippe
  International Journal of Fatigue, Elsevier, 2019, 121, pp.84-97. The fatigue performance of coarse and ultrafine-grained (UFG) 5083 Al alloy were compared, from low to very high cycle fatigue. The UFG alloy exhibited cyclic hardening and predominant kinematic hardening. At high plastic strain amplitude (and only in this regime), it showed easier crack initiation and a lower fatigue resistance. Its resistance to HCF was hardly better than that of its coarse grained counterpart until 2.10 6 cycles, but 43% higher in VHCF, until 5.10 8 cycles. Beyond that point, internal crack initiation occurred, and the fatigue resistance of the UFG material decreased, which was explained using Fracture Mechanics. (10.1016/j.ijfatigue.2018.12.004)
  DOI : 10.1016/j.ijfatigue.2018.12.004
• Plastic zone evolution during fatigue crack growth: Digital image correlation coupled with finite elements method
  
  • Hosdez Jérôme
  • Langlois Mederic
  • Witz J-F
  • Limodin N.
  • Najjar D.
  • Charkaluk E.
  • Osmond P.
  • Forre A.
  • Szmytka F.
  International Journal of Solids and Structures, Elsevier, 2019, 171, pp.92-102. Nonlinearities effects at the crack tip, due to the elastic-plastic material behavior , impact the crack growth rate and path. This paper is devoted to the study of the plastic zone evolution in the crack tip region. The methodology relies on coupling an elastic-plastic Finite Elements Method (FEM) model and experimental displacements measured by Digital Image Correlation (DIC). These latter are introduced as Dirichlet boundary conditions in the finite elements analysis. The considered FEM domain is constant, i.e. the same mesh with a centered crack is moved to each new crack tip position deduced from DIC. The new boundary conditions are updated and the residual stresses and plastic strains of the former computation are interpolated and actualized on the mesh shifted to the new crack tip position in order to incorporate them in the numerical model. The coupling method allowed applying experimental boundary conditions in order to be as close as possible to real experimental conditions and to observe the plasticity evolution from small to large scale yielding conditions. A fatigue test was conducted to validate the proposed approach. The identification residues are proved to be lower than those obtained with an experimental displacements projection onto Williams' series basis, which is a method commonly used with DIC. The coupling results present an attractive similarity with Irwin's model regardless of the crack length. Thus, the definition of the mask needed for the displacements fields projection on Williams' model can be deduced with a reliable estimate of Irwin's plastic radius. (10.1016/j.ijsolstr.2019.04.032)
  DOI : 10.1016/j.ijsolstr.2019.04.032
• Stochastic modeling of chemical-mechanical coupling in striated muscles
  
  • Caruel Matthieu
  • Moireau Philippe
  • Chapelle Dominique
  Biomechanics and Modeling in Mechanobiology, Springer Verlag, 2019. We propose a chemical-mechanical model of myosin heads in sarcomeres, within the classical description of rigid sliding filaments. In our case, myosin heads have two mechanical degrees-of-freedom (dofs) - one of which associated with the so-called power stroke - and two possible chemical states, i.e. bound to an actin site or not. Our major motivations are twofold: (1) to derive a multiscale coupled chemical-mechanical model, and (2) to thus account - at the macroscopic scale - for mechanical phenomena that are out of reach for classical muscle models. This model is first written in the form of Langevin stochastic equations, and we are then able to obtain the corresponding Fokker-Planck partial differential equations governing the probability density functions associated with the mechanical dofs and chemical states. This second form is important, as it allows to monitor muscle energetics, and also to compare our model with classical ones, such as the Huxley'57 model to which our equations are shown to reduce under two different types of simplifying assumptions. This provides insight, and gives a Langevin form for Huxley'57. We then show how we can calibrate our model based on experimental data - taken here for skeletal muscles - and numerical simulations demonstrate the adequacy of the model to represent complex physiological phenomena, in particular the fast isometric transients in which the power stroke is known to have a crucial role, thus circumventing a limitation of many classical models. (10.1007/s10237-018-1102-z)
  DOI : 10.1007/s10237-018-1102-z
• A micromechanical inspired model for the coupled to damage elasto-plastic behavior of geomaterials under compression
  
  • Marigo Jean-Jacques
  • Kazymyrenko Kyrylo
  Mechanics & Industry, EDP Sciences, 2019, 20 (1), pp.105. We propose an elasto-plastic model coupled with damage for the behavior of geomaterials in compression. The model is based on the properties, shown in [S. Andrieux, et al., Un modèle de matériau microfissuré pour les bétons et les roches, J. Mécanique Théorique Appliquée 5 (1986) 471?513], of microcracked materials when the microcracks are closed with a friction between their lips. That leads to a macroscopic model coupling damage and plasticity where the plasticity yield criterion is of the Drucker–Prager type with kinematical hardening. Adopting an associative flow rule for the plasticity and a standard energetic criterion for damage, the properties of such a model are illustrated in a triaxial test with a fixed confining pressure. (10.1051/meca/2018043)
  DOI : 10.1051/meca/2018043
• Calcium and plasma membrane force-gated ion channels behind development
  
  • Frachisse Jean-Marie
  • Thomine Sébastien
  • Allain Jean-Marc
  Current Opinion in Plant Biology, Elsevier, 2019, 53, pp.57--64. During development, tissues are submitted to high variation of compression and tension forces. The roles of the cell wall, the cytoskeleton, the turgor pressure and the cell geometry during this process have received due attention. In contrast, apart from its role in the establishment of turgor pressure, the involvement of the plasma membrane as a transducer of mechanical forces during development has been under studied. Force-gated (FG) or Mechanosensitive (MS) ion channels embedded in the bilayer represent 'per se' archetypal mechanosensor able to directly and instantaneously transduce membrane forces into electrical and calcium signals. We discuss here how their fine-tuning, combined with their ability to detect micro-curvature and local membrane tension, allows FG channels to transduce mechanical cues into developmental signals. (10.1016/j.pbi.2019.10.006)
  DOI : 10.1016/j.pbi.2019.10.006
• Fatigue Crack Initiation and Propagation
  
  • Doquet Véronique
  • Hénaff Gilbert
  • Palin-Luc Thierry
  • Risbet Marion
  , 2019, pp.65-90. The resistance of metal alloys to fatigue can be classified into four major regimes: low-cycle fatigue (or short life), limited resistance (between 10^5 and 10^6 cycles), high-cycle fatigue (between 10^6 and 10^7 cycles) and gigacycle (more than 10^7 cycles). This chapter introduces the basic concepts of cyclic mechanical behavior, crack initiation and propagation in these different regimes. (10.1016/b978-1-78548-309-7.50004-1)
  DOI : 10.1016/b978-1-78548-309-7.50004-1
• Plastic intermittency during cyclic loading: From dislocation patterning to microcrack initiation
  
  • Weiss J.
  • Rhouma W Ben
  • Deschanel S.
  • Truskinovsky L.
  Physical Review Materials, American Physical Society, 2019, 3. In metallic materials subjected to cyclic loading, strain hardening as well as fatigue crack initiation have been linked for a long time with the evolution of dislocation patterns and structures. In particular, the development of low-energy dislocation configurations such as persistent slip bands (PSBs) is considered as a precursor to crack initiation. However, the associated scenarios have been elaborated mainly from postmortem observations capturing only static pictures of dislocation patterns, while the dynamics of the problem has been somewhat overlooked. Here we analyze collective dislocation dynamics during cycling loading of aluminum using acoustic emission (AE). A strong link is revealed between dislocation patterning, cyclic hardening/softening, and the intermittency of plasticity: Plastic intermittency and dislocation avalanches rapidly decay during the initial hardening stage, in conjunction with the reduction of an internal length scale characterizing the dislocation structure. However, in nonannealed samples, a transient softening stage ensues, associated with a brutal reorganization of this structure. These initial stages of cyclic deformation illustrate the competition between two phenomena: collective dislocation dynamics, governed by long-ranged elastic interactions among dislocations, and the emergence of a self-organizing network controlled by short-range interactions and progressively inhibiting collective effects. Later on, the emergence of PSBs is accompanied by a reincrease of the AE intermittent activity. We propose that the associated AE bursts may be the signature of collective and coordinated dislocation motions along PSBs leading to the formation of incipient microcracks. (10.1103/PhysRevMaterials.3.023603)
  DOI : 10.1103/PhysRevMaterials.3.023603
• Numerically-aided 3D printed random isotropic porous materials approaching the Hashin-Shtrikman bounds
  
  • Zerhouni O.
  • Tarantino M.G. G
  • Danas K.
  Composites Part B: Engineering, Elsevier, 2019, 156, pp.344 - 354. The present study introduces a methodology that allows to combine 3D printing, experimental testing, numerical and analytical modeling to create random closed-cell porous materials with statistically controlled and isotropic overall elastic properties that are extremely close to the relevant Hashin-Shtrikman bounds. In this first study, we focus our experimental and 3D printing efforts to isotropic random microstructures consisting of single-sized (i.e. monodisperse) spherical voids embedded in a homogeneous solid matrix. The 3D printed specimens are realized by use of the random sequential adsorption method. A detailed FE numerical study allows to define a cubic representative volume element (RVE) by combined periodic and kinematically uniform (i.e. average strain or affine) boundary conditions. The resulting cubic RVE is subsequently assembled to form a standard dog-bone uniaxial tension specimen, which is 3D printed by use of a photopolymeric resin material. The specimens are then tested at relatively small strains by a proper multi-step relaxation procedure to obtain the effective elastic properties of the porous specimens. (10.1016/j.compositesb.2018.08.032)
  DOI : 10.1016/j.compositesb.2018.08.032
• Continuum theory of bending-to-stretching transition
  
  • Salman O.U.
  • Vitale G
  • Truskinovsky Lev
  Physical Review E, American Physical Society (APS), 2019, 100 (5), pp.051001. Transition from bending-dominated to stretching-dominated elastic response in semiflexible fibrous networks plays an important role in the mechanical behavior of cells and tissues. It is induced by changes in network connectivity and relies on the construction of new cross-links. We propose a simple continuum model of this transition with macroscopic strain playing the role of order parameter. An unusual feature of this Landau-type theory is that it is based on a single-well potential. The theory predicts that bending-to-stretching transition should proceed through propagation of the fronts separating domains with affine and nonaffine elastic response. (10.1103/PhysRevE.100.051001)
  DOI : 10.1103/PhysRevE.100.051001
• Buckling and post-buckling of plates
  
  • Audoly Basile
  • Altenbach Holm
  • Öchsner Andreas
  , 2019. (10.1007/978-3-662-53605-6)
  DOI : 10.1007/978-3-662-53605-6
• Analysis and numerical simulation of an inverse problem for a structured cell population dynamics model
  
  • Clément Frédérique
  • Laroche Béatrice
  • Robin Frédérique
  Mathematical Biosciences and Engineering, AIMS Press, 2019, 16 (4), pp.3018-3046. In this work, we study a multiscale inverse problem associated with a multi-type model for age structured cell populations. In the single type case, the model is a McKendrick-VonFoerster like equation with a mitosis-dependent death rate and potential migration at birth. In the multi-type case, the migration term results in an unidirectional motion from one type to the next, so that the boundary condition at age 0 contains an additional extrinsic contribution from the previous type. We consider the inverse problem of retrieving microscopic information (the division rates and migration proportions) from the knowledge of macroscopic information (total number of cells per layer), given the initial condition. We first show the well-posedness of the inverse problem in the single type case using a Fredholm integral equation derived from the characteristic curves, and we use a constructive approach to obtain the lattice division rate, considering either a synchronized or non-synchronized initial condition. We take advantage of the unidirectional motion to decompose the whole model into nested submodels corresponding to self-renewal equations with an additional extrinstic contribution. We again derive a Fredholm integral equation for each submodel and deduce the well-posedness of the multi-type inverse problem. In each situation, we illustrate numerically our theoretical results. (10.3934/mbe.2019150)
  DOI : 10.3934/mbe.2019150
• Front shape similarity measure for data-driven simulations of wildland fire spread based on state estimation: Application to the RxCADRE field-scale experiment
  
  • Zhang Cong
  • Collin Annabelle
  • Moireau Philippe
  • Trouvé Arnaud
  • Rochoux Mélanie C.
  Proceedings of the Combustion Institute, Elsevier, 2019, 37 (3), pp.4201-4209. Data-driven wildfire spread modeling is emerging as a cornerstone for forecasting real-time fire behavior using thermal-infrared imaging data. One key challenge in data assimilation lies in the design of an adequate measure to represent the discrepancies between observed and simulated firelines (or "fronts"). A first approach consists in adopting a Lagrangian description of the flame front and in computing a Euclidean distance between simulated and observed fronts by pairing each observed marker with its closest neighbor along the simulated front. However, this front marker registration approach is difficult to generalize to complex front topology that can occur when fire propagation conditions are highly heterogeneous due to topography, biomass fuel and micrometeorology. To overcome this issue, we investigate in this paper an object-oriented approach derived from the Chan-Vese contour fitting functional used in image processing. The burning area is treated as a moving object that can undergo shape deformations and topological changes. We combine this non-Euclidean measure with a state estimation approach (a Luenberger observer) to perform simulations of the time-evolving fire front location driven by discrete observations of the fireline. We apply this object-oriented data assimilation method to the three-hectare RxCADRE S5 field-scale experiment. We demonstrate that this method provides more accurate forecast of fireline propagation than if either the fire spread model or the observations were taken separately. Results show that when the observation frequency becomes lower than 1/60 s −1 , the forecast performance of data assimilation is improved compared to simply extrapolating observation data. This highlights the need of a physics-based forward model to forecast flame front propagation. We also demonstrate that the front shape similarity measure is suitable for both Eulerian and Lagrangian-type front-tracking solvers and thereby can provide a unified framework to track moving structures such as flame front position and topology in combustion problems. (10.1016/j.proci.2018.07.112)
  DOI : 10.1016/j.proci.2018.07.112
• Aggregate-driven reconfigurations of carbon nanotubes in thin networks under strain: in-situ characterization
  
  • Bodelot Laurence
  • Pavic Luka
  • Hallais Simon
  • Charliac Jérôme
  • Lebental Bérengère
  Scientific Reports, Nature Publishing Group, 2019, pp.11p. This work focuses on the in-situ characterization of multi-walled carbon nanotube (CNT) motions in thin random networks under strain. Many fine-grain models have been devised to account for CNT motions in carbon nanotube networks (CNN). However, the validation of these models relies on mesoscopic or macroscopic data with very little experimental validation of the physical mechanisms actually arising at the CNT scale. In the present paper, we use in-situ scanning electron microscopy imaging and high resolution digital image correlation to uncover prominent mechanisms of CNT motions in CNNs under strain. Results show that thin and sparse CNNs feature stronger strain heterogeneities than thicker and denser ones. It is attributed to the complex motions of individual CNTs connected to aggregates within thin and sparse CNNs. While the aggregates exhibit a collective homogeneous deformation, individual CNTs connecting them are observed to fold, unwind or buckle, seemingly to accommodate the motion of these aggregates. In addition, looser aggregates feature internal reconfgurations via cell closing, similar to foam materials. Overall, this suggests that models describing thin and sparse CNN deformation should integrate multiphase behaviour (with various densities of aggregates in addition to individual CNTs), heterogeneity across surface, as well as imperfect substrate adhesion. (10.1038/s41598-019-41989-2)
  DOI : 10.1038/s41598-019-41989-2
• Computational quantification of patient specific changes in ventricular dynamics associated with pulmonary hypertension
  
  • Finsberg Henrik Nicolay Topnes
  • Sundnes Joakim
  • Xi Ce
  • Lee Lik Chuan
  • Zhao Xiaodan
  • Tan Ju Le
  • Genet Martin
  • Zhong Liang
  • Wall Samuel Thomas
  AJP - Heart and Circulatory Physiology, American Physiological Society, 2019. Pulmonary arterial hypertension causes an increase in the mechanical loading imposed on the right ventricle that results in progressive changes to its mechanics and function. Here, we quantify the mechanical changes associated with PAH by assimiliating clinical data consisting of reconstructed 3D geometry, pressure and volume waveforms as well as regional strains measured in PAH patients (n = 12) and controls (n = 6) within a computational modeling framework of the ventricles. Modeling parameters reflecting regional passive stiness and load-independent contractility as indexed by the tissue active tension were optimized so that simulation results matched the measurements The optimized parameters were compared with clinical metrics to and usable indicators associated with the underlying mechanical changes. Peak contractility of the RV free wall γRWFW,max was found to be strongly correlated, and had an inverse relationship with the RV and left ventricle end-diastolic volume ratio (i.e., RVEDV/LVEDV) (γRWFW,max=-0.13(RVEDV/LVEDV)+0.44, R2=0.77). Correlation with RV ejection fraction (R2=0.5) and end-diastolic volume index (R2=0.4) were comparatively weaker. Patients with RVEDV/LVEDV≤1.5 had 18% higher γRWFW,max (P = 0.09) than that of the control whereas those with RVEDV/LVEDV > 1.5 had 25% lower γRWFW,max (P<0.05). On average, RVFW passive stiffness increased progressively with the degree of remodeling as indexed by RVEDV/LVEDV and RVFW myofiber stress was increased by 49% only in patients with RVEDV/LVEDV ≥ 1.5 (P = 0.14). These results provide the mechanical basis of using RVEDV/LVEDV as a clinical index for delineating disease severity and estimating RVFW contractility in PAH patients. (10.1152/ajpheart.00094.2019)
  DOI : 10.1152/ajpheart.00094.2019
• Thermodynamic properties of muscle contraction models and associated discrete-time principles
  
  • Kimmig François
  • Chapelle Dominique
  • Moireau Philippe
  Advanced Modeling and Simulation in Engineering Sciences, Springer, 2019, 6. Considering a large class of muscle contraction models accounting for actin-myosin interaction, we present a mathematical setting in which solution properties can be established, including fundamental thermodynamic balances. Moreover, we propose a complete discretization strategy for which we are also able to obtain discrete versions of the thermodynamic balances and other properties. Our major objective is to show how the thermodynamics of such models can be tracked after discretization, including when they are coupled to a macroscopic muscle formulation in the realm of continuum mechanics. Our approach allows to carefully identify the sources of energy and entropy in the system, and to follow them up to the numerical applications. (10.1186/s40323-019-0128-9)
  DOI : 10.1186/s40323-019-0128-9