Publications

2018

• Validation of cardiac strain estimation from 3D-tagged magnetic resonance images using finite element image correlation
  
  • Berberoglu Ezgi
  • Stoeck Christian T
  • Kozerke Sebastian
  • Genet Martin
  , 2018.
• Solving 2D linear isotropic elastodynamics by means of scalar potentials: a new challenge for finite elements
  
  • Albella Martínez Jorge
  • Imperiale Sébastien
  • Joly Patrick
  • Rodríguez Jerónimo
  Journal of Scientific Computing, Springer Verlag, 2018. In this work we present a method for the computation of numerical solutions of 2D homogeneous isotropic elastodynamics equations by solving scalar wave equations. These equations act on the potentials of a Helmholtz decomposition of the displacement field and are decoupled inside the propagation domain. We detail how these equations are coupled at the boundary depending on the nature of the boundary condition satisfied by the displacement field. After presenting the case of rigid boundary conditions, that presents no specific difficulty, we tackle the challenging case of free surface boundary conditions that presents severe stability issues if a straightforward approach is used. We introduce an adequate functional framework as well as a time domain mixed formulation to circumvent these issues. Numerical results confirm the stability of the proposed approach. (10.1007/s10915-018-0768-9)
  DOI : 10.1007/s10915-018-0768-9
• Front shape similarity measure for shape-oriented sensitivity analysis and data assimilation for Eikonal equation
  
  • Rochoux Mélanie
  • Collin Annabelle
  • Zhang Cong
  • Trouvé Arnaud
  • Lucor Didier
  • Moireau Philippe
  ESAIM: Proceedings and Surveys, EDP Sciences, 2018, pp.258 - 279. We present a shape-oriented data assimilation strategy suitable for front-tracking problems through the example of wildfire. The concept of " front " is used to model, at regional scales, the burning area delimitation that moves, undergoes shape and topological changes under heterogeneous orography, biomass fuel and micrometeorology. The simulation-observation discrepancies are represented using a front shape similarity measure deriving from image processing and based on the Chan-Vese contour fitting functional. We show that consistent corrections of the front location and uncertain physical parameters can be obtained using this measure applied on a level-set fire growth model solving for an eikonal equation. This study involves a Luenberger observer for state estimation, including a topological gradient term to track multiple fronts, and of a reduced-order Kalman filter for joint parameter estimation. We also highlight the need – prior to parameter estimation – for sensitivity analysis based on the same discrepancy measure, and for instance using polynomial chaos metamodels, to ensure a meaningful inverse solution is achieved. The performance of the shape-oriented data assimilation strategy is assessed on a synthetic configuration subject to uncertainties in front initial position, near-surface wind magnitude and direction. The use of a robust front shape similarity measure paves the way toward the direct assimilation of infrared images and is a valuable asset in the perspective of data-driven wildfire modeling. (10.1051/proc/201863258)
  DOI : 10.1051/proc/201863258
• A Discrete-time Optimal Filtering Approach for Non-linear Systems as a Stable Discretization of the Mortensen Observer
  
  • Moireau Philippe
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2018, 24 (4), pp.1815 - 1847. In this work, we seek exact formulations of the optimal estimator and filter for a non-linear framework, as the Kalman filter is for a linear framework. The solution is well established with the Mortensen filter in a continuous-time setting, but we seek here its counterpart in a discrete-time context. We demonstrate that it is possible to pursue at the discrete-time level an exact dynamic programming strategy and we find an optimal estimator combining a prediction step using the model and a correction step using the data. This optimal estimator reduces to the discrete-time Kalman estimator when the operators are in fact linear. Furthermore, the strategy that consists of discretizing the least square criterion and then finding the exact estimator at the discrete level allows to determine a new time-scheme for the Mortensen filter which is proven to be consistent and unconditionally stable, with also a consistent and stable discretization of the underlying Hamilton-Jacobi-Bellman equation. (10.1051/cocv/2017077)
  DOI : 10.1051/cocv/2017077
• Mechanical stress as a regulator of cell motility
  
  • Putelat T.
  • Recho Pierre
  • Truskinovsky L.
  Physical Review E, American Physical Society (APS), 2018, 97 (1). (10.1103/physreve.97.012410)
  DOI : 10.1103/physreve.97.012410
• Newton-Krylov method for computing the cyclic steady states of evolution problems in non-linear mechanics
  
  • Khristenko Ustim
  • Le Tallec Patrick
  International Journal for Numerical Methods in Engineering, Wiley, 2018. This work is focused on the Newton‐Krylov technique for computing the steady cyclic states of evolution problems in non‐linear mechanics with space‐time periodicity conditions. This kind of problems can be faced, for instance, in the modeling of a rolling tyre with a periodic tread pattern, where the cyclic state satisfies "rolling" periodicity condition, including shifts both in time and space. The Newton‐Krylov method is a combination of a Newton nonlinear solver with a Krylov linear solver, looking for the initial state, which provides the space‐time periodic solution. The convergence of the Krylov iterations is proved to hold in presence of an adequate preconditioner. After preconditioning, the Newton‐Krylov method can be also considered as an observer‐controller method, correcting the transient solution of the initial value problem after each period. Using information stored while computing the residual, the Krylov solver computation time becomes negligible with respect to the residual computation time. The method has been analyzed and tested on academic applications and compared to the standard evolution (fixed point) method. Finally, it has been implemented into the Michelin industrial code, applied to a full 3D rolling tyre model. (10.1002/nme.5920)
  DOI : 10.1002/nme.5920
• Fatigue of Additive Manufacturing Specimens: A Comparison with Casting Processes
  
  • Charkaluk Eric
  • Chastand Victor
  Proceedings, MDPI, 2018, 2 (8). (10.3390/ICEM18-05352)
  DOI : 10.3390/ICEM18-05352
• Equilibrated warping: Finite element image registration with finite strain equilibrium gap regularization
  
  • Genet Martin
  • Stoeck C. T
  • von Deuster C.
  • Lee L. C.
  • Kozerke S.
  Medical Image Analysis, Elsevier, 2018, 50, pp.1-22. In this paper, we propose a novel continuum finite strain formulation of the equilibrium gap regularization for image registration. The equilibrium gap regularization essentially penalizes any deviation from the solution of a hyperelastic body in equilibrium with arbitrary loads prescribed at the boundary. It thus represents a regularization with strong mechanical basis, especially suited for cardiac image analysis. We describe the consistent linearization and discretization of the regularized image registration problem, in the framework of the finite elements method. The method is implemented using FEniCS & VTK, and distributed as a freely available python library. We show that the equilibrated warping method is effective and robust: regularization strength and image noise have minimal impact on motion tracking, especially when compared to strain-based regularization methods such as hyperelastic warping. We also show that equilibrated warping is able to extract main deformation features on both tagged and untagged cardiac magnetic resonance images. (10.1016/j.media.2018.07.007)
  DOI : 10.1016/j.media.2018.07.007
• Extra Corporeal Life Support for Cardiac ARrest patients with post-cardiac arrest syndrome: the ECCAR study
  
  • Bouglé Adrien
  • Le Gall Arthur
  • Dumas Florence
  • Geri Guillaume
  • Malissin Isabelle
  • Voicu Sebastian
  • Mégarbane Bruno
  • Cariou Alain
  • Deye Nicolas
  Archives of cardiovascular diseases, Elsevier ; Société française de cardiologie [2008-....], 2018. Purpose: Post-Cardiac Arrest Shock (PCAS) occurring after resuscitated cardiac arrest (CA), is a main cause of early death. Extra-Corporeal Life Support (ECLS) could be useful pending recovery of myocardial failure. We aimed to describe our PCAS population, and factors associated with ECLS initiation. Materials and Methods: This analysis included 924 patients admitted in two intensive care units (ICU) between 2005 and 2014 for CA and PCAS, and, of those patients, 43 patients for whom an ECLS was initiated. Neurological and ECLS-related outcomes were gathered retrospectively. Results: The 43 ECLS patients were predominantly young males with evidence of myocardial infarction on coronary angiography (70%). ECLS was initiated in patients suffering from severe cardiovascular dysfunction (Left Ventricular Ejection Fraction: 15 [10 -25] %), with a median delay of 9 [6 -16] hours following CA. At one year, 8 patients survived (19%) without neurological disability. Blood lactate and coronary etiology were associated with neurological outcomes. Logistic regression conducted using 878 PCAS controls identified age, sex, current smoking, location of CA, blood lactate and creatinine levels as risk factors for initiation of ECLS. Conclusions: ECLS, as a salvage therapy for PCAS, could represent an acceptable alternative for highly selected patients.
• STUDY OF THE INFLUENCE OF SMALL DEFECTS NEAR A SINGULAR POINT IN ANTIPLANE ELASTICITY BY AN ASYMPTOTIC METHOD
  
  • Dang Thi Bach Tuyet
  Vietnam Journal of Mechanics, Viện Hàn Lâm Khoa học và Công nghệ Việt Nam, 2018. (10.15625/0866-7136/9341)
  DOI : 10.15625/0866-7136/9341
• Proceedings of the Cemracs 2016 - numerical challenges in parallel scientific computing.
  
  • Grigori Laura
  • Japhet Caroline
  • Moireau Philippe
  , 2018, 63, pp.I-III. (10.1051/proc/20186300i)
  DOI : 10.1051/proc/20186300i
• Comparative study of fatigue properties of Ti-6Al-4V specimens built by electron beam melting (EBM) and selective laser melting (SLM)
  
  • Chastand Victor
  • Quaegebeur Philippe
  • Maia Wilson
  • Charkaluk Eric
  Materials Characterization, Elsevier, 2018, 143, pp.76-81. Electron Beam Melting (EBM) and Selective Laser Melting (SLM) are two of the most developed powder bed fusion based additive manufacturing processes. In this paper, fatigue properties of Ti-6Al-4V specimens built by EBM and SLM are compared. Several parameters are assessed: processes, manufacturing direction, surface roughness, HIP treatment. Fatigue properties are analyzed in relation with the crack initiation mechanisms identified on each specimen's post-mortem micrographs. Machined specimens show better fatigue properties as surface defects are removed. HIP treatment improves fatigue properties by decreasing the defects size. Small differences in lifetime are observed between horizontal and vertical building directions because of different defect shapes regarding the loading axis. Finally, EBM and SLM parts have approximately the same fatigue properties, which are equivalent to conventional casting processes. (10.1016/j.matchar.2018.03.028)
  DOI : 10.1016/j.matchar.2018.03.028
• Mixed mode II and III fatigue crack growth in a rail steel
  
  • Bonniot Thomas
  • Doquet Véronique
  • Mai Si Hai
  International Journal of Fatigue, Elsevier, 2018, 115, pp.42-52. Rolling contact fatigue cracks in rails undergo non-proportional mixed-mode I+II+III, in variable proportions along their front. In order to determine the crack growth thresholds and kinetics in mixed-mode II/III, asymmetric four point bending tests are run on a rail steel with different angles between the crack front and the shearing load, so as to vary the mode mixity ratio. For sufficiently high loading ranges, these tests give rise to coplanar shear-mode crack growth. The effective stress intensity factors (SIFs) are derived by an inverse method from the measured crack face relative displacements. It appears to be 10–70% lower than the nominal SIFs and to allow a reasonable correlation of the measured crack growth rates. The local application, ahead of the crack front, of shear-driven or tension-driven fatigue damage models – after 3D elastic-plastic computations of local stress and strain ranges – allows a successful prediction of crack fronts paths and growth rates. (10.1016/j.ijfatigue.2018.01.010)
  DOI : 10.1016/j.ijfatigue.2018.01.010
• Experimental homogenized elastic properties of computer-generated 3D-printed random porous material
  
  • Zerhouni O.
  • Tarantino M G
  • Danas K.
  , 2018. The present study introduces a methodology that allows for the combination of 3D-printing, experimental testing, numerical and analytical analysis of random porous materials with controlled homogenized elastic properties. These microstructures are computer-generated based on a random sequential addition algorithm with statistically controlled morphological properties such as volume fraction, shape and size of voids as well as isotropic distribution of their centers. We first focus on porous material containing single-size (monodisperse) spherical voids. The porous specimens are fabricated by 3D printing with polymer jet technology and then microstructures are aposteriori investigated by optical microscopy and SEM. The influence of the 3D printing process parameters is also experimentally assessed. An experimental protocol is developed in order to obtain the effective elastic properties of the porous specimens.
• Efficient estimation of personalized biventricular mechanical function employing gradient-based optimization
  
  • Finsberg Henrik
  • Xi Ce
  • Tan Ju Le
  • Zhong Liang
  • Genet Martin
  • Sundnes Joakim
  • Lee Lik Chuan
  • Wall Samuel
  International Journal for Numerical Methods in Biomedical Engineering, John Wiley and Sons, 2018, 34 (7), pp.e2982. Individually personalized computational models of heart mechanics can be used to estimate important physiological and clinically-relevant quantities that are difficult, if not impossible, to directly measure in the beating heart. Here, we present a novel and efficient framework for creating patient-specific biventricular models using a gradient-based data assimilation method for evaluating regional myocardial contractility and estimating myofiber stress. These simulations can be performed on a regular laptop in less than 2 h and produce excellent fit between measured and simulated volume and strain data through the entire cardiac cycle. By applying the framework using data obtained from 3 healthy human biventricles, we extracted clinically important quantities as well as explored the role of fiber angles on heart function. Our results show that steep fiber angles at the endocardium and epicardium are required to produce simulated motion compatible with measured strain and volume data. We also find that the contraction and subsequent systolic stresses in the right ventricle are significantly lower than that in the left ventricle. Variability of the estimated quantities with respect to both patient data and modeling choices are also found to be low. Because of its high efficiency, this framework may be applicable to modeling of patient specific cardiac mechanics for diagnostic purposes. (10.1002/cnm.2982)
  DOI : 10.1002/cnm.2982
• An adaptive Hybridizable Discontinuous Galerkin approach for cardiac electrophysiology
  
  • Hoermann Julia
  • Bertoglio Cristóbal
  • Kronbichler Martin
  • Pfaller Martin
  • Chabiniok Radomir
  • Wall Wolfgang
  International Journal for Numerical Methods in Biomedical Engineering, John Wiley and Sons, 2018, 34 (5), pp.e2959 (20 pages). Cardiac electrophysiology simulations are numerically challenging due to the propagation of a steep electrochemical wave front and thus require discretizations with small mesh sizes to obtain accurate results. In this work, we present an approach based on the Hybridizable Discontinuous Galerkin method (HDG), which allows an efficient implementation of high-order discretizations into a computational framework. In particular using the advantage of the discontinuous function space, we present an efficient p-adaptive strategy for accurately tracking the wave front. HDG allows to reduce the overall degrees of freedom in the final linear system to those only on the element interfaces. Additionally, we propose a rule for a suitable integration accuracy for the ionic current term depending on the polynomial order and the cell model to handle high-order polynomials. Our results show that for the same number of degrees of freedom coarse high-order elements provide more accurate results than fine low-order elements. Introducing p-adaptivity further reduces computational costs while maintaining accuracy by restricting the use of high-order elements to resolve the wave front. For a patient-specific simulation of a cardiac cycle p-adaptivity reduces the average number of degrees of freedom by 95% compared to the non-adaptive model. In addition to reducing computational costs, using coarse meshes with our p-adaptive high-order HDG method also simplifies practical aspects of mesh generation and postprocessing. (10.1002/cnm.2959)
  DOI : 10.1002/cnm.2959
• Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model
  
  • Collin Annabelle
  • Imperiale Sébastien
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2018. The aim of this paper is to provide a complete mathematical analysis of the periodic homogenization procedure that leads to the macroscopic bidomain model in cardiac elec-trophysiology. We consider space-dependent and tensorial electric conductivities as well as space-dependent physiological and phenomenological non-linear ionic models. We provide the nondimensionalization of the bidomain equations and derive uniform estimates of the solutions. The homogenization procedure is done using 2-scale convergence theory which enables us to study the behavior of the non-linear ionic models in the homogenization process . (10.1142/S0218202518500264)
  DOI : 10.1142/S0218202518500264
• Experimental investigation of elastomer mode I fracture: an attempt to estimate the critical strain energy release rate using SENT tests
  
  • Roucou David
  • Diani Julie
  • Brieu Mathias
  • Witz Jean-Francois
  • Mbiakop-Ngassa Armel
  International Journal of Fracture, Springer Verlag, 2018, 209 (1-2), pp.163 - 170. The resistance to mode I failure of rubbers is studied by submitting single edge notch samples to uniaxial tension. Reproducing the seminal work of Rivlin and Thomas (J Polym Sci 10:291–318, 1953), single edge notch tension specimens, presenting notches of various lengths, are stretched until break. A styrene butadiene rubber, unfilled and filled with carbon-black, and an unfilled rubber from the latter mentioned work, were considered. When the notch is smaller than one fifth of the sample width, mode I crack opening is observed, leading to catastrophic failure that creates smooth mirror-like crack surfaces. Nonetheless, the experimental force-elongation responses show that the mode I critical energy release rate cannot be calculated by a classical Griffith elastic failure analysis. When notches are longer, the SENT samples are not submitted to pure uniaxial tension only. Structural bending leads to uncontrolled mixed mode crack propagation. The surfaces created when the long notches propagate are rough and bifurcations are witnessed for the filled rubbers. (10.1007/s10704-017-0251-x)
  DOI : 10.1007/s10704-017-0251-x
• The importance of the pericardium for cardiac biomechanics: From physiology to computational modeling
  
  • Pfaller Martin
  • Hoermann Julia
  • Weigl Martina
  • Nagler Andreas
  • Chabiniok Radomir
  • Bertoglio Cristóbal
  • Wall Wolfgang A.
  Biomechanics and Modeling in Mechanobiology, Springer Verlag, 2018. The human heart is enclosed in the pericardial cavity. The pericardium consists of a layered thin sac and is separated from the myocardium by a thin film of fluid. It provides a fixture in space and friction-less sliding of the myocardium. The influence of the pericardium is essential for predictive mechanical simulations of the heart. However, there is no consensus on physiologically correct and computationally tractable pericardial boundary conditions. Here we propose to model the pericardial influence as a parallel spring and dashpot acting in normal direction to the epicardium. Using a four-chamber geometry, we compare a model with pericardial boundary conditions to a model with fixated apex. The influence of pericardial stiffness is demonstrated in a parametric study. Comparing simu-lation results to measurements from cine magnetic resonance imaging reveals that adding pericardial boundary conditions yields a better approximation with respectto atrioventricular plane displacement, atrial filling, and overall spatial approximation error. We demonstrate that this simple model of pericardial-myocardial interaction can correctly predict the pumping mechanisms ofthe heart as previously assessed in clinical studies. Utilizing a pericardial model can not only provide much more realistic cardiac mechanics simulations but also allows new insights into pericardial-myocardial interaction which cannot be assessed in clinical measurement.
• Airborne ultrasound surface motion camera: application to seismocardiography
  
  • Shirkovskiy Pavel
  • Laurin Alexandre
  • Jeger-Madiot Nathan
  • Chapelle Dominique
  • Fink Mathias
  • Ing Ros Kiri
  Applied Physics Letters, American Institute of Physics, 2018, 112. The recent achievements in the accelerometer-based seismocardiography field indicate a strong potential for this technique to address wide variety of clinical needs. Recordings from different locations on the chest can give a more comprehensive observation and interpretation of wave propagation phenomena than a single-point recording, can validate existing modeling assumptions (such as the representation of the sternum as a single solid body), and provide better identifiability for models using richer recordings. Ultimately, the goal is to advance our physiological understanding of the processes to provide useful data to promote cardiovascular health. Accelerometer-based multichannel system is a contact method and laborious for use in practice, also even ultralight accelerometers can cause non-negligible loading effects. We propose a new contactless ultrasound imaging method to measure thoracic and abdominal surface motions, demonstrating that it is adequate for typical seismocardiogram use. The developed method extends non-contact surface-vibrometry to fast 2D mapping by originally combining multi-element airborne ultrasound arrays, a synthetic aperture implementation and pulsed-waves. Experimental results show the ability of the developed method to obtain 2D seismocardiographic maps of the body surface 30×40 cm 2 in dimension, with a temporal sampling rate of several hundred Hz, using ultrasound waves with the central frequency of 40 kHz. Our implementation was validated in-vivo on eight healthy human participants. The shape and position of the zone of maximal absolute acceleration and velocity during the cardiac cycle were also observed. This technology could potentially be used to obtain more complete cardio-vascular information than single-source SCG in and out of clinical environments, due to enhanced identifiability provided by distributed measurements, and observation of propagation phenomena. (10.1063/1.5028348)
  DOI : 10.1063/1.5028348
• Advances in computational modeling approaches of pituitary gonadotropin signaling
  
  • Yvinec Romain
  • Crépieux Pascale
  • Reiter Eric
  • Poupon Anne
  • Clément Frédérique
  Expert Opinion on Drug Discovery, Informa Healthcare, 2018, 13 (9), pp.799-813. Pituitary gonadotropins play an essential and pivotal role in the control of human and animal reproduction within the hypothalamic-pituitary-gonadal (HPG) axis. The computational modeling of pituitary gonadotropin signaling encompasses phenomena of different natures such as the dynamic encoding of gonadotropin secretion, and the intracellular cascades triggered by gonadotropin binding to their cognate receptors, resulting in a variety of biological outcomes. We overview historical and ongoing issues in modeling and data analysis related to gonadotropin secretion in the field of both physiology and neuro-endocrinology. We mention the different mathematical formalisms involved, their interest and limits. We discuss open statistical questions in signal analysis associated with key endocrine issues. We also review recent advances in the modeling of the intracellular pathways activated by gonadotropins, which yields promising development for innovative approaches in drug discovery. The greatest challenge to be tackled in computational modeling of pituitary gonadotropin signaling is the embedding of gonadotropin signaling within its natural multi-scale environment, from the single cell level, to the organic and whole HPG level. The development of modeling approaches of G protein-coupled receptor signaling, together with multicellular systems biology may lead to unexampled mechanistic understanding with critical expected fallouts in the therapeutic management of reproduction. (10.1080/17460441.2018.1501025)
  DOI : 10.1080/17460441.2018.1501025
• A conservative penalisation strategy for the semi-implicit time discretisation of incompressible elastodynamics equation
  
  • Caforio Federica
  • Imperiale Sébastien
  Advanced Modeling and Simulation in Engineering Sciences, Springer, 2018, 5 (1), pp.1-27. The principal aim of this work is to provide an adapted numerical scheme for the approximation of elastic wave propagation in incompressible solids. We rely on high-order conforming finite element with mass lumping for space discretisation and implicit/explicit, second-order, energy-preserving time discretisation. The time step restriction only depends on the shear wave velocity and at each time step a Poisson problem must be solved to account for the incompressibility constraint that is imposed by penalisation techniques.
• In-situ experimental and numerical studies of the damage evolution and fracture in a Fe-TiB2 composite
  
  • Hadjem-Hamouche Zehoua
  • Derrien Katell
  • Héripré Eva
  • Chevalier Jean-Pierre
  Materials Science and Engineering: A, Elsevier, 2018, 724, pp.594-605.. A joint experimental and modelling study of plastic strain and ensuing damage in a novel metal matrix composite (Fe-TiB2) is presented. Damage is observed and quantified using SEM images processing and Acoustic Emission (AE) analysis. The use of AE confirms that the surface damage observed is strongly correlated to damage in the bulk of the material. The primary mode of damage is particle fracture. Very little particle decohesion is observed, indicating an exceptionally good cohesion of the steel/particle interface. Damage is initiated soon after the composite yield point is reached and increases significantly with strain. Macroscopic failure of the tensile specimen occurs when about 25% of the particles are fractured. This corresponds to about 21% engineering strain. Using in-situ SEM tensile tests with quantitative digital image correlation (DIC), full-field strain measurements are obtained and particle fracture quantified. The results of fields measurements are compared to results of a FFT based homogenization method with boundary conditions retrieved from the experiment. A good agreement is found between the DIC-measured and FFT-predicted results. Estimated values of the particle fracture stress are obtained. (10.1016/j.msea.2018.03.108)
  DOI : 10.1016/j.msea.2018.03.108
• Wetting by liquid sodium and fracture path analysis of sodium induced embrittlement of 304L stainless steel
  
  • Barkia Bassem
  • Auger Thierry
  • Courouau Jean Louis
  • Bourgon Julie
  Journal of Materials Research, Springer, 2018, 33 (2), pp.121-129. The wettability of the 304L steel is an important parameter in Liquid Metal Embrittlement studies. Empirically, it is found to be greatly enhanced by pre-exposure to oxygenated liquid sodium. The corrosion interface formed during exposure to sodium has been analyzed at the nanoscale by transmission electron microscopy using the focused ion beam sampling. A thin layer of sodium chromite (Na xCrO2 with x ≤ 1) is detected at the interface validating wetting on an oxide mechanism for the enhanced wetting after pre-exposure. Fracture micromechanisms and the crack path of liquid sodium-embrittled austenitic steel 304L at 573 K have been investigated down to the nanoscale. High-resolution orientation mapping analyses immediately below the fracture surface show that abundant martensitic transformations (γ → α) and twinning occur during deformation of austenite. The preferential crack path is intergranular along the newly formed γ/γ interfaces. It is concluded that these transformations play a major role in the fracture process. (10.1557/jmr.2017.435)
  DOI : 10.1557/jmr.2017.435
• Strain-gradient vs damage-gradient regularizations of softening damage models
  
  • Le Duc Trung
  • Marigo Jean-Jacques
  • Maurini Corrado
  • Vidoli Stefano
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2018, 340, pp.424-450. Local damage models with softening needs localization limiters to preserve the mathematical and physical consistency. In this paper we compare the properties of strain-gradient and damage-gradient regularizations. Gradient-damage models introduce a quadratic dependency of the dissipated energy on the gradient of the damage field and are nowadays extensively used as phase-field approximation of brittle fracture. Their key feature is to provide a smeared approximation of a crack as a band of localised damage with a finite energy dissipation per unit of surface, that can be identified with the fracture toughness of the Griffith model. Strain gradient models introduce a quadratic dependence of the elastic energy on the gradient of the strain field. A similar term can be physically interpreted as the presence in the material of linear, but nonlocal, stiffnesses, that can be eventually be affected by damage. Despite this attractive interpretation, we have found that strain-gradient regularized models can hardly be used to approximate brittle fracture, because smeared cracks with non-vanishing and finite dissipated energies are hardly obtained. Our analysis is based on variational models and focuses on the one-dimensional traction problem. (10.1016/j.cma.2018.06.013)
  DOI : 10.1016/j.cma.2018.06.013