Publications

2019

• 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
• 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
• Dispositif cardiaque
  
  • Chapelle Dominique
  • Moireau Philippe
  • Pernot Mathieu
  • Tanter Mickael
  , 2019.
• A relaxed growth modeling framework for controlling growth-induced residual stresses
  
  • Genet Martin
  Clinical Biomechanics, Elsevier, 2019. Background. Constitutive models of the mechanical response of soft tissues have been established and are widely accepted, but models of soft tissues remodeling are more controversial. Specifically for growth, one important question arises pertaining to residual stresses: existing growth models inevitably introduce residual stresses, but it is not entirely clear if this is physiological or merely an artifact of the modeling framework. As a consequence, in simulating growth, some authors have chosen to keep growth-induced residual stresses, and others have chosen to remove them. Methods. In this paper, we introduce a novel “relaxed growth” framework allowing for a fine control of the amount of residual stresses generated during tissue growth. It is a direct extension of the classical framework of the multiplicative decomposition of the transformation gradient, to which an additional sub-transformation is introduced in order to let the original unloaded configuration evolve, hence relieving some residual stresses. We provide multiple illustrations of the framework mechanical response, on time-driven constrained growth as well as the strain-driven growth problem of the artery under internal pressure, including the opening angle experiment. Findings. The novel relaxed growth modeling framework introduced in this paper allows for a better control of growth-induced residual stresses compared to standard growth models based on the multiplicative decomposition of the transformation gradient. Interpretation. Growth-induced residual stresses should 1 be better handled in soft tissues biomechanical models, especially in patient-specific models of diseased organs that are aimed at augmented diagnosis and treatment optimization. (10.1016/j.clinbiomech.2019.08.015)
  DOI : 10.1016/j.clinbiomech.2019.08.015
• Review and analysis of historical leakages from storage salt caverns wells
  
  • Bérest Pierre
  • Réveillère Arnaud
  • Evans David
  • Stöwer Markus
  Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles, Institut Français du Pétrole (IFP), 2019, 74, pp.27. Twelve incidents involving well casing and/or cement leaks in the salt caverns storage industry are described. These incidents occurred at the following storage sites: Eminence salt dome, Mississippi; Elk City, Oklahoma; Conway, Kansas; Yoder, Kansas; Mont Belvieu, Texas; Teutschenthal/Bad Lauchstädt, Germany; Clute, Texas; Mineola, Texas; Hutchinson, Kansas; Magnolia, Louisiana; Boling, Texas; Epe, Germany. Mechanisms leading to a casing leak and consequences are discussed. In most cases, a breach in a steel casing occurred at a depth where a single casing was isolating the stored product from the geological formations. The origin of the breach was due in most cases to poor welding/screwing conditions and corrosion, or excessive deformation of the rock formation. In this, the age of the well is often influential. In many cases, the leak path does not open directly at ground level; fugitive hydrocarbons first escape and accumulate in the subsurface prior to migrating through shallower horizons and escaping at ground surface. A pressure differential between hydrocarbons in the borehole and fluids in the rock mass favours fast leak rates. A wellhead pressure drop often is observed, even when the stored product is natural gas. The incidents described suggest that thorough monitoring (tightness tests) and a correct well design would lessen considerably the probability of a casing leak occurring. (10.2516/ogst/2018093)
  DOI : 10.2516/ogst/2018093
• Uniaxial compression of calcite single crystals at room temperature: insights into twinning activation and development
  
  • Parlangeau Camille
  • Dimanov Alexandre
  • Lacombe Olivier
  • Hallais Simon
  • Daniel Jean-Marc
  Solid Earth, European Geosciences Union, 2019, 10 (1), pp.307-316. E-twinning is a common plastic deformation mechanism in calcite deformed at low temperature. Strain rate, temperature and confining pressure have negligible effects on twinning activation which is mainly dependent on differential stress. The critical resolved shear stress (CRSS) required for twinning activation is dependent on grain size and strain hardening. This CRSS value may obey the Hall–Petch relation, but due to sparse experimental data its actual evolution with grain size and strain still remains a matter of debate. In order to provide additional constraints on twinning activation and development, new mechanical tests were carried out at room temperature on unconfined single crystals of calcite, with different sizes and crystallographic orientations. Uniaxial deformation was performed at a controlled displacement rate, while the sample surface was monitored using optical microscopy and a high-resolution CCD (charge-coupled device) camera. The retrieved macroscopic stress–strain behavior of the crystals was correlated with the surface observations of the deformation process. Results show (1) the onset of crystal plasticity with the activation of the first isolated mechanical twins during the strain hardening stage, and (2) the densification and thickening of twin lamellae during the steady-state flow stress stage. Such thickening of twin lamellae at room temperature emphasizes that calcite twin morphology is not controlled solely by temperature. The different values for the CRSS obtained for the activation of isolated twins and for the onset of twin densification and thickening raises questions regarding the appropriate value to be considered when using calcite twin data for stress inversion purposes. (10.5194/se-10-307-2019)
  DOI : 10.5194/se-10-307-2019
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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