Publications

2020

• Energetic upscaling strategy for grain growth. I: Fast mesoscopic model based on dissipation
  
  • Sakout Sofia
  • Weisz-Patrault Daniel
  • Ehrlacher Alain
  Acta Materialia, Elsevier, 2020, 196, pp.261-279. Tailoring microstructures by optimizing fabrication or forming processes is a challenge for metal industries. However, predicting microstructure evolution implies to develop models at the scale of the polycrystal, which is incompatible with large scale simulations of processes. In this context, we propose an energetic upscaling strategy to model anisotropic grain growth at large scale without loosing detailed grains statistics. Thus, a fast mesoscopic model is necessary to establish a large database of computations in order to develop a macroscopic model whose state variables contain statistical descriptors of the microstructure. This paper focuses on a fast mesoscopic model based on Voronoi-Laguerre tessellations, which are updated at each time step to capture grain growth. Several energetic contributions are considered at different scales. The grain boundary energy is obtained as a function of misorientation from molecular dynamics, and the dissipated power is obtained from crystal plasticity theory. The evolution law at the mesoscopic scale is obtained by considering all energetic contributions in the representative volume element, and from thermodynamic laws and approximate mass conservation. This upscaling approach reaches short computation time, which is essential to establish the database underlying the macroscopic model. Basic grain statistics are validated by comparison to classical models. Moreover, a good agreement is observed with an experiment conducted on pure iron. The model is then used to analyze the evolution of detailed statistics. To capture grain growth at macroscopic scale, it is necessary to consider couplings between means and standard deviations of various distributions (e.g., size, shape, misorientation etc. (10.1016/j.actamat.2020.06.032)
  DOI : 10.1016/j.actamat.2020.06.032
• Estimation of patient-specific mechanical parameters in pulmonary diseases
  
  • Patte Cécile
  • Brillet Pierre-Yves
  • Fetita Catalin
  • Gille Thomas
  • Bernaudin Jean-François
  • Nunes Hilario
  • Chapelle Dominique
  • Genet Martin
  , 2020.
• On a reduced cylindrical model of the left ventricular dynamics
  
  • Genet Martin
  • Diaz J
  • Chapelle D
  • Moireau Philippe
  , 2020.
• Intrinsic regulation of muscle contraction
  
  • Kimmig François
  • Caruel M
  • Chapelle D
  , 2020.
• A one-dimensional model for elasto-capillary necking
  
  • Lestringant Claire
  • Audoly Basile
  Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, Royal Society, The, 2020, 476 (2240), pp.20200337. We derive a non-linear one-dimensional (1d) strain gradient model predicting the necking of soft elastic cylinders driven by surface tension, starting from 3d finite-strain elasticity. It is asymptotically correct: the microscopic displacement is identified by an energy method. The 1d model can predict the bifurcations occurring in the solutions of the 3d elasticity problem when the surface tension is increased, leading to a localization phenomenon akin to phase separation. Comparisons with finite-element simulations reveal that the 1d model resolves the interface separating two phases accurately, including well into the localized regime, and that it has a vastly larger domain of validity than 1d model proposed so far. (10.1098/rspa.2020.0337)
  DOI : 10.1098/rspa.2020.0337
• Influence of interlayer dwell time on the microstructure of Inconel 718 Laser Cladded components
  
  • Guévenoux Camille
  • Hallais Simon
  • Charles Alexandre
  • Charkaluk Eric
  • Constantinescu Andrei
  Optics and Laser Technology, Elsevier, 2020, 128, pp.106218. Laser Cladding is one of the leading additive manufacturing technologies enabling the repair of metallic components. Their fatigue reliability depends directly on the material microstructure and consequently on the process parameters. This study highlights the influence of the interlayer dwell time on single-track walls for Inconel 718 repaired components. EBSD analyses show that dwell time both reduces grain size and creates a textural stretch of the microstructure. An optimal dwell time between the writing of successive layers can then be introduced to target a specified microstruc-ture gradient at the interface between the original part and the repaired deposit. (10.1016/j.optlastec.2020.106218)
  DOI : 10.1016/j.optlastec.2020.106218
• Application of Synchrotron Radiation–Computed Tomography In-Situ Observations and Digital Volume Correlation to Study Low-Cycle Fatigue Damage Micromechanisms in Lost Foam Casting A319 Alloy
  
  • Wang Long
  • Limodin N.
  • El Bartali Ahmed
  • Witz Jean-Francois
  • Buffiere Jean-Yves
  • Charkaluk Eric
  Metallurgical and Materials Transactions A, Springer Verlag/ASM International, 2020, 51 (8), pp.3843-3857. The synchrotron radiation–computed tomography (SR-CT) and digital volume correlation (DVC) methods were used to investigate the damage micromechanisms of lost foam casting (LFC) A319 alloy in low-cycle fatigue (LCF). LCF tests with SR-CT in-situ observations allow visualizing the damage evolution process in the bulk. DVC measures the mechanical fields and, thus, allows establishing the relations between crack initiation and propagation, mechanical fields, and microstructure. Cracks initiate at and propagate along hard inclusions due to strain localizations. The damage process, i.e., crack initiation and propagation, can be considered as a series of failure events of hard inclusions under strain localizations. The pores’ size, shape, location, and number were observed to have an influence on crack initiation, while the interconnected hard inclusion networks guarantee the continuous failure events of hard inclusions and, thus, provide crack propagation paths. (10.1007/s11661-020-05839-5)
  DOI : 10.1007/s11661-020-05839-5
• Thermal modeling of DED repair process for slender panels by a 2D semi-analytic approach
  
  • Guévenoux Camille
  • Nasiry Mohamad
  • Durbecq Sylvain
  • Charles Alexandre
  • Charkaluk Eric
  • Constantinescu Andrei
  , 2020. Directed Energy Deposition is one of the leading additive manufacturing technologies tailored for the repair of metallic components. The spatial and temporal pattern of the heat flux results in specific thermal gradients and cooling rates, controlling the final microstructure and mechanical properties of the repaired component. Simplified thermal analyses based on Rosenthal's solution offers an interesting way to model in short computational times the repair process of simple geometries, estimating the spatial thermal gradients or cooling rates. This article presents a new model based on Rosenthal's solution. Compared to other existing analytic solutions, the present work contains material layer addition and therefore enables the modeling of not only one layer but of the complete additive manufacturing process. The validity domain of the model is identified using experimental measurements on 316L stainless steel. Possible applications are also provided: determination of solidification regime (columnar or equiaxed grains) in solidification maps or optimization of the duration of interlayer dwell time needed to keep the part under a low annealing temperature.
• Analytical and experimental study of the identification strategy in magnetic resonance imaging
  
  • Kurtz Samuel
  • Geymonat Giuseppe
  • Krasucki Françoise
  • van Houten Elijah
  • Wattrisse Bertrand
  , 2020. Magnetic Resonance Elastography (MRE) is a modality that allows the mapping of the mechanical properties of soft tissues such as brain or liver from Magnetic Resonance Imaging (MRI) data. Specific MRI sequences have been developed in order to estimate the 3D displacement field in biological tissues undergoing harmonic solicitations [1]. The aim of this work consists in comparing the performance of different identification methods proposed for MRE in a situation straightforward enough –while still representative of elastography applications– to permit both analytic and experimental approaches. For the sake of simplicity, we present only the homogeneous case. The mechanical analysis of the problem illustrated in Figure 1 leads, for an adapted set of boundary conditions, to the resolution of the following usual problem. (voir annexe) For a given set of experimental conditions, we determine the complex-valued solution fields. The so-obtained displacement fields can be perturbed to represent experimental noise. These modified displacements are then introduced as input for different identification methods (Finite Element Model Updating [2], Constitutive Equation Gap [3] or Modified Constitutive Equation Gap [4]) in order to characterize their different efficiencies. In parallel, experimental tests are performed on gelatin samples with “controlled” properties in order to characterize these methods using real data.
• Hierarchical modeling of force generation in cardiac muscle
  
  • Kimmig François
  • Caruel Matthieu
  Biomechanics and Modeling in Mechanobiology, Springer Verlag, 2020, 19, pp.2567–2601. Performing physiologically relevant simulations of the beating heart in clinical context requires to develop detailed models of the microscale force generation process. These models however may reveal difficult to implement in practice due to their high computational costs and complex calibration. We propose a hierarchy of three interconnected muscle contraction models-from the more refined to the more simplified-that are rigorously and systematically related with each other, offering a way to select, for a specific application, the model that yields a good trade-off between physiological fidelity, computational cost and calibration complexity. The three models families are compared to the same set of experimental data to systematically assess what physiological indicators can be reproduced or not and how these indicators constrain the model parameters. Finally, we discuss the applicability of these models for heart simulation. (10.1007/s10237-020-01357-w)
  DOI : 10.1007/s10237-020-01357-w
• High Prevalence of Deep Vein Thrombosis in Mechanically Ventilated COVID-19 Patients
  
  • Voicu Sebastian
  • Bonnin Philippe
  • Stépanian Alain
  • Chousterman Benjamin
  • Le Gall Arthur
  • Malissin Isabelle
  • Deye Nicolas
  • Siguret Virgine
  • Mebazaa Alexandre
  • Mégarbane Bruno
  Journal of the American College of Cardiology, Elsevier, 2020, 76 (4), pp.480-482. (10.1016/j.jacc.2020.05.053)
  DOI : 10.1016/j.jacc.2020.05.053
• Energy Localization through Locally Resonant Materials
  
  • Moscatelli Marco
  • Comi Claudia
  • Marigo Jean-Jacques
  Materials, MDPI, 2020, 13 (13), pp.3016. Among the attractive properties of metamaterials, the capability of focusing and localizing waves has recently attracted research interest to establish novel energy harvester configurations. In the same frame, in this work, we develop and optimize a system for concentrating mechanical energy carried by elastic anti-plane waves. The system, resembling a Fabry-Pérot interferometer, has two barriers composed of Locally Resonant Materials (LRMs) and separated by a homogeneous internal cavity. The attenuation properties of the LRMs allow for the localization of waves propagating at particular frequencies. With proper assumptions on the specific ternary LRMs, the separation of scales (between the considered wave lengths and the characteristic dimension of the employed unit cells) enables the use of a two-scale asymptotic technique for computing the effective behavior of the employed LRMs. This leads to a complete analytic description of the motion of the system. Here we report the results achieved by optimizing the geometry of the system for obtaining a maximum focusing of the incoming mechanical energy. The analytic results are then validated through numerical simulations. (10.3390/ma13133016)
  DOI : 10.3390/ma13133016
• Multi-partner benchmark experiment of fatigue crack growth measurements
  
  • Langlois Raphaël
  • Cusset Raphaël
  • Hosdez Jerome
  • Bonnand Vincent
  • Blaysat Benoît
  • Menut-Tournadre Léa
  • Neggers Jan
  • Coret Michel
  • Henry Joseph
  • Doquet Véronique
  • Grediac Michel
  • Chiaruttini Vincent
  • Poncelet Martin
  • Proudhon Henry
  • Limodin Nathalie
  • Réthoré Julien
  Engineering Fracture Mechanics, Elsevier, 2020, 235. The design of reliable structures and the estimation of the residual fatigue life of industrial parts containing flaws or cracks rely on our ability to predict the propagation of fatigue cracks. Whereas in industrial component cracks might have a complex path due to geometry and loading, lab experiments used for identifying crack propagation law are often in pure mode I. The paper presents a synthesis of an experimental benchmark performed in the context of a French national research network. A sample has been designed to produce mixed-mode crack propagation and variation of small scale yielding conditions. Two geometries and two maximum load levels are defined for the two tested materials: a stainless steel and an aluminum alloy. Around ten participants performed experiments using their usual instrumentation. Among the eight possible parameter sets, three are selected for which detailed results are presented. A satisfying overall agreement is obtained. But, some discrepancies are evidenced due either to limitations of the instrumentation or simply because from one lab to the other the applied load is not exactly the same. It is thus concluded that one of the most important issue is boundary conditions, which is confirmed by numerical simulations. (10.1016/j.engfracmech.2020.107157)
  DOI : 10.1016/j.engfracmech.2020.107157
• Self-heating behavior during cyclic loadings of 316L stainless steel specimens manufactured or repaired by Directed Energy Deposition
  
  • Balit Yanis
  • Joly Louis-Romain
  • Szmytka Fabien
  • Durbecq Sylvain
  • Charkaluk Eric
  • Constantinescu Andrei
  Materials Science and Engineering: A, Elsevier, 2020, 786, pp.139476. The purpose of this article is to assess a self-heating testing method for the characterization of fatigue properties of single-track thickness additively manufactured specimens. It also evaluates the impact of the microstructure orientation with respect to the loading direction on the dissipative behavior and the initiation of microcracks. The 316L stainless steel specimens under scrutiny were manufactured by Directed Energy Deposition in two configurations: (i) fully printed specimens (2 orientations) and (ii) repaired specimens. The paper first presents a morphologic and crystallographic texture analysis and second, a series of self-heating tests under cyclic loading. The mi-crostructural analysis revealed elongated grains with their sizes, shapes and preferred orientations controlled by process parameters. The self-heating measurements under cyclic tensile loading proved that the dissipation estimation through infrared measurements can be performed on small scale, thin specimens. The self-heating curves could successfully be represented by the Munier model. Moreover, several links between the printing parameters and self-heating results could be established. For example, a smaller vertical increment between successively deposited layers leads to higher mean (10.1016/j.msea.2020.139476)
  DOI : 10.1016/j.msea.2020.139476
• A constitutive model for a rate and temperature-dependent, plastically anisotropic titanium alloy
  
  • Ruiz de Sotto Miguel
  • Longère Patrice
  • Doquet Véronique
  • Papasidero Jessica
  International Journal of Plasticity, Elsevier, 2020, pp.102777. Aircraft engine fan blades are notably designed to withstand impact loading involving large deformation, high strain rate, non-proportional loading paths and self-heating. Due to their high strength-to-weight ratio and good toughness, Ti–6Al–4V titanium alloys are promising candidates for the blades leading edge. An extensive experimental campaign on a Ti–6Al–4V titanium alloy provided in the form of cold rolled plates has been carried out. The thermo-mechanical characterization consisted in tension, compression and shear tests performed at various strain rates and temperatures, and under monotonic as well as alternate loading paths. A constitutive model has been accordingly developed accounting for the combined effect of plastic orthotropy and tension/compression asymmetry, nonlinear isotropic and kinematic strain hardening, strain rate hardening, and thermal softening. The constitutive model has been implemented as a user material subroutine into the commercial finite element computation code LS-DYNA. The performances of the model have been estimated by conducting numerical simulations considering a volume element under various loading paths as well as the specimens used for the experimental campaign. (10.1016/j.ijplas.2020.102777)
  DOI : 10.1016/j.ijplas.2020.102777
• Monitoring of cardiovascular physiology augmented by a patient-specific biomechanical model during general anesthesia. A proof of concept study
  
  • Le Gall Arthur
  • Vallée Fabrice
  • Pushparajah Kuberan
  • Hussain Tarique
  • Mebazaa Alexandre
  • Chapelle Dominique
  • Gayat Etienne
  • Chabiniok Radomir
  PLoS ONE, Public Library of Science, 2020. During general anesthesia (GA), direct analysis of arterial pressure or aortic flow waveforms may be inconclusive in complex situations. Patient-specific biomechanical models, based on data obtained during GA and capable to perform fast simulations of cardiac cycles, have the potential to augment hemodynamic monitoring. Such models allow to simulate Pressure-Volume (PV) loops and estimate functional indicators of cardiovascular (CV) system, e.g. ventricular-arterial coupling (Vva), cardiac efficiency (CE) or myocardial contractility, evolving throughout GA. In this prospective observational study, we created patient-specific biomechanical models of heart and vasculature of a reduced geometric complexity for n=45 patients undergoing GA, while using transthoracic echocardiography and aortic pressure and flow signals acquired in the beginning of GA (baseline condition). If intraoperative hypotension (IOH) appeared, diluted norepinephrine (NOR) was administered and the model readjusted according to the measured aortic pressure and flow signals. Such patients were a posteriori assigned into a so-called hypotensive group. The accuracy of simulated mean aortic pressure (MAP) and stroke volume (SV) at baseline were in accordance with the guidelines for the validation of new devices or reference measurement methods in all patients. After NOR administration in the hypotensive group, the percentage of concordance with 10% exclusion zone between measurement and simulation was > 95% for both MAP and SV. The modeling results showed a decreased Vva (0.64±0.37 vs 0.88±0.43; p=0.039) and an increased CE (0.8±0.1 vs 0.73±0.11; p=0.042) in hypotensive vs normotensive patients. Furthermore, Vva increased by 92±101%, CE decreased by 13±11% (p < 0.001 for both) and contractility increased by 14±11% (p = 0.002) in the hypotensive group post-NOR administration. In this work we demonstrated the application of fast-running patient-specific biophysical models to estimate PV loops and functional indicators of CV system using clinical data available during GA. The work paves the way for model-augmented hemodynamic monitoring at operating theatres or intensive care units to enhance the information on patient-specific physiology. (10.1371/journal.pone.0232830)
  DOI : 10.1371/journal.pone.0232830
• A nonlinear beam model of photomotile structures
  
  • Korner Kevin
  • Kuenstler Alexa S
  • Hayward Ryan C
  • Audoly Basile
  • Bhattacharya Kaushik
  Proceedings of the National Academy of Sciences of the United States of America, National Academy of Sciences, 2020, 117 (18), pp.9762. Actuation remains a significant challenge in soft robotics. Actuation by light has important advantages: Objects can be actuated from a distance, distinct frequencies can be used to actuate and control distinct modes with minimal interference, and significant power can be transmitted over long distances through corrosion-free, lightweight fiber optic cables. Photochemical processes that directly convert photons to configurational changes are particularly attractive for actuation. Various works have reported light-induced actuation with liquid crystal elastomers combined with azobenzene photochromes. We present a simple model-ing framework and a series of examples that study actuation by light. Of particular interest is the generation of cyclic or periodic motion under steady illumination. We show that this emerges as a result of a coupling between light absorption and deformation. As the structure absorbs light and deforms, the conditions of illumination change, and this, in turn, changes the nature of further deformation. This coupling can be exploited in either closed structures or with structural instabilities to generate cyclic motion. (10.1073/pnas.1915374117)
  DOI : 10.1073/pnas.1915374117
• CHENILLE : Coupled beHaviour undErstaNdIng of fauLts : from the Laboratory to the fiEld
  
  • Bonnelye Audrey
  • Dick Pierre
  • Lüth Stefan
  • Henninges Jan
  • Kwiatek Grzegorz
  • Scleicher Anja
  • Dimanov Alexandre
  • Fortin Jérôme
  • Cotton Fabrice
  , 2020. &lt;p&gt;The understanding of the coupled thermo-hydro-mechanical behaviour of fault zones is of fundamental importance for a variety of societal and economic reasons, such as the sustainable energy transition for the safe use of natural resources (energy storage, nuclear waste disposal or geothermal energy). The overall objective of this inter-disciplinary project is to create a dataset that will allow to highlight the physical processes resulting from a thermal and hydric load on an existing, identified and characterized fault zone.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;An in situ experiment will be performed at IRSN&amp;#8217;s Tournemire Underground Research Laboratory to evaluate the hydraulic properties and mechanical behaviour of a fault zone in a shale formation due to an increase of gas or water pressure under incremental thermal loading. This fracturing field tests will be conducted using four types of boreholes drilled from the URL : (i) one injection borehole (INJ) with one chamber measuring 10 m in length; (ii) four boreholes (H1 to H4) dedicated to host steel canister electrical&amp;#160;heaters, (iii) 5 boreholes (S1 to S5) dedicated to the geophysical monitoring of seismic and aseismic fracturing processes, (iv) two to four boreholes (M1 to M4) to record deformation and estimate fracture location, which will help assess the seismic survey. After an initial saturation phase of the chamber, successive sequences of fluid injection tests are planned. The preliminary injection tests will be done stepwise either at constant flow or at constant pressure rate in order to obtain a steady-state flow regime at normal in situ temperatures. The hydraulic conductivity and permeability of the fault zone will be then inferred. A second stage of hydraulic testing will involve the determination of the main hydraulic parameters during a stepwise increase of temperature within the volume (maximum temperature 150&amp;#176;C). In the meantime, the seismological responses of the injected structures, from the static deformation to the high-frequency (100-kHz) acoustic emissions will be surveyed. The evolution of temperature and deformation will be monitored thanks to fibre optic array. In addition, a controlled seismic experiment is proposed, using coupled magnetostrictive vibrators to investigate the structural environment before and after experiment.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;Moreover, to accompany the field study, a series of laboratory experiments will be conducted to understand the chemical and structural evolution occurring within fault zones during the thermal and hydraulic loading. Experiments in climatic chambers exposing the samples to the same heat treatment as that of the in situ experiment will be carried out in order to compare the mineralogical composition evolution of the samples with those taken from the field investigated zone. Finally, a rock mechanical study, from the microscopic to the centimeter scale with monitoring of the acoustic properties will be carried out. This study will include experiments from Scanning Electron Microscope with Energy Dispersive Spectroscopy (SEM-EDS) allowing the identification of the micro-scale mechanisms of deformation localization to which it is planned to add an acoustic measurement system. In order to study the evolution of mechanical behaviour as a function of scale, experiments in triaxial press, again with acoustic monitoring, are planned.&lt;/p&gt; (10.5194/egusphere-egu2020-13477)
  DOI : 10.5194/egusphere-egu2020-13477
• Fatigue crack growth under non-proportional mixed-mode I + II. Role of compression while shearing
  
  • Bonniot Thomas
  • Doquet Véronique
  • Mai Si Hai
  International Journal of Fatigue, Elsevier, 2020, 134, pp.105513. Mode I + II fatigue crack growth tests are run, following sequential or pseudo-sequential loading paths, representative of those computed for ”squat type” cracks in rails. Stereo DIC provides the near-tip displacements,from which ΔKIeffective and ΔKIIeffective are derived. Compression while shearing extends coplanar growth, by slowing down the wear-induced rise of the effective mode mixity ratio, up to the critical value for which bifurcation occurs. The consideration of plasticity and contact and friction stresses improves crack paths predictions,compared to the maximum tangential stress criterion. The coplanar crack growth rate correlates well with a combination of ΔKIeffective and ΔKIIeffective (10.1016/j.ijfatigue.2020.105513)
  DOI : 10.1016/j.ijfatigue.2020.105513
• Effective mechanical response of non-linear heterogeneous materials comprising bimodular phases
  
  • Monaldo Elisabetta
  • Brach Stella
  • Kondo Djimedo
  • Vairo Giuseppe
  European Journal of Mechanics - A/Solids, Elsevier, 2020, 81, pp.103962. In this study, the effective constitutive behavior of heterogeneous materials comprising bimodular phases is investigated through a computational approach and by referring to Curnier-type bimodularity. Different microstructures characterized by spherical inclusions or voids are addressed, by analyzing different loading scenarios. Numerical results, obtained via an iterative finite-element scheme, highlight the influence of intraphase constitutive non-linearities induced by the tension/compression transition of the local material stiffness. Moreover, coupling effects between hydrostatic and deviatoric states are elucidated. The macroscale material response results dependent on the loading condition, and it is driven by perturbative effects of heterogeneous fields locally induced by pores or inclusions. (10.1016/j.euromechsol.2020.103962)
  DOI : 10.1016/j.euromechsol.2020.103962
• Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations
  
  • Chabassier Juliette
  • Diaz Julien
  • Imperiale Sébastien
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2020, 54 (3), pp.845-878. This paper deals with the construction of a family of fourth order, energy consistent, explicit time discretizations for dissipative linear wave equations. The schemes are obtained by replacing the inversion of a matrix, that comes naturally after using the technique of the Modified Equation on the second order Leap Frog scheme applied to dissipative linear wave equations, by explicit approximations of its inverse. The stability of the schemes are studied using an energy analysis and a convergence analysis is carried out. Numerical results in 1D illustrate the space/time convergence properties of the schemes and their efficiency is compared to more classical time discretizations. (10.1051/m2an/2019079)
  DOI : 10.1051/m2an/2019079
• Microstructurally-guided explicit continuum models for isotropic magnetorheological elastomers with iron particles
  
  • Mukherjee Dipayan
  • Bodelot Laurence
  • Danas Kostas
  International Journal of Non-Linear Mechanics, Elsevier, 2020, 120, pp.103380. This work provides a family of explicit phenomenological models both in the F − H and F − B variable space. These models are derived directly from an analytical implicit homogenization model for isotropic magnetorheological elastomers (MREs), which, in turn, is assessed via full-field numerical simulations. The proposed phenomenological models are constructed so that they recover the same purely mechanical, initial and saturation magnetization and initial magnetostriction response of the analytical homogenization model for all sets of material parameters, such as the particle volume fraction and the material properties of the constituents (e.g., the matrix shear modulus, the magnetic susceptibility and magnetization saturation of the particles). The functional form of the proposed phenomenological models is based on simple energy functions with small number of calibration parameters thus allowing for the description of magnetoelastic solids more generally such as anisotropic (with particle-chains) ones, polymers comprising ferrofluid particles or particle clusters. This, in turn, makes them suitable to probe a large set of experimental or numerical results. The models of the present study show that in isotropic MREs, the entire magnetization response is insensitive to the shear modulus of the matrix material even when the latter ranges between 0.003-0.3MPa, while the magnetostriction response is extremely sensitive to the mechanical properties of the matrix material. (10.1016/j.ijnonlinmec.2019.103380)
  DOI : 10.1016/j.ijnonlinmec.2019.103380
• A discrete, geometrically exact method for simulating nonlinear, elastic or non-elastic beams
  
  • Lestringant Claire
  • Audoly Basile
  • Kochmann Dennis
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2020, 361, pp.112741. We present an extension of a discrete, geometrically exact beam formulation originally introduced in the computer graphics community, as well as an implementation that fits naturally in existing finite element programs. This numerical method is variational, fully decouples the kinematics from the material behavior, and can handle finite rotations as well as a wide class of constitutive laws depending on the stretching, flexural and torsional strain and strain rates. We demonstrate its capabilities through a suite of benchmark problems involving elastic, viscous and visco-elastic beams. The method is well suited to engineering applications, and can e ciently and accurately simulate the nonlinear deformation of slender beams featuring complex material behavior, such as those found in the topical design of truss metamaterials. (10.1016/j.cma.2019.112741)
  DOI : 10.1016/j.cma.2019.112741
• Localization in spherical shell buckling
  
  • Audoly Basile
  • Hutchinson John
  Journal of the Mechanics and Physics of Solids, Elsevier, 2020, 136, pp.103720. This paper addresses localization of the deformation due to buckling that occurs immediately following the onset of bifurcation in the axisymmetric buckling of a perfect spherical elastic shell subject to external pressure. The localization process is so abrupt that the buckling mode of the classical eigenvalue analysis, which undulates over the entire shell, becomes modified immediately after bifurcation transitioning to an isolated dimple surrounded by an unbuckled expanse of the shell. The paper begins by revisiting earlier attempts to analyze the initial post-buckling behavior of the spherical shell, illustrating their severely limited range of validity. The unsuccessful attempts are followed by an approximate Rayleigh-Ritz solution which captures the essence of the localization process. The approximate solution reveals the pathway that begins at bifurcation from the classical mode shape to the localized dimple buckle. The second part of the paper presents an exact asymptotic expansion of the initial post-buckling behavior which accounts for localization and which further exposes the analytic details of the abruptness of the transition. (10.1016/j.jmps.2019.103720)
  DOI : 10.1016/j.jmps.2019.103720
• Two families of explicit models constructed from a homogenization solution for the magnetoelastic response of MREs containing iron and ferrofluid particles
  
  • Lefèvre Victor
  • Danas Kostas
  • Lopez-Pamis Oscar
  International Journal of Non-Linear Mechanics, Elsevier, 2020, 119, pp.103362. This work puts forth two families of fully explicit continuum or phenomenological models that are constructed by approximating an analytical (but implicit) homogenization solution recently derived for the free-energy function describing the macroscopic magnetoelastic response of two classes of MREs comprised of an isotropic incompressible elastomer filled with a random isotropic distribution of: i) spherical iron particles and ii) spherical ferrofluid particles. Both families are given in terms of free-energy functions W H = W H (F, H) that depend on the deformation gradient F and the Lagrangian magnetic field H and are constructed so as to agree identically with the homogenization solution for small and large applied magnetic fields, this for arbitrary finite deformations and arbitrary volume fractions c of particles in the entire physical range c ∈ [0, 1]. The accuracy of the proposed phenomenological models is assessed inter alia via the direct comparison of their predictions with that of the homogenization solution for a boundary-value problem of both fundamental and practical significance: the magnetostriction response of a spherical MRE specimen subject to a remotely applied uniform magnetic field. (10.1016/j.ijnonlinmec.2019.103362)
  DOI : 10.1016/j.ijnonlinmec.2019.103362