Publications

2017

• Numerical modeling of the acoustic wave propagation across an homogenized rigid microstructure in the time domain
  
  • Lombard Bruno
  • Maurel Agnes
  • Marigo Jean-Jacques
  Journal of Computational Physics, Elsevier, 2017, 335, pp.558-577. Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded. This paper aims (i) to propose a numerical method able to handle the jump conditions in order to simulate the homogenized problem in the time domain, (ii) to inspect the validity of the homogenized problem when compared to the real one. For this purpose, we adapt the Explicit Simplified Interface Method originally developed for standard jump conditions across a zero-thickness interface. Doing so allows us to handle arbitrary-shaped interfaces on a Cartesian grid with the same efficiency and accuracy of the numerical scheme than those obtained in an homogeneous medium. Numerical experiments are performed to test the properties of the numerical method and to inspect the validity of the homogenization problem. (10.1016/j.jcp.2017.01.036)
  DOI : 10.1016/j.jcp.2017.01.036
• Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: one-dimensional examples
  
  • Alessi Roberto
  • Marigo Jean-Jacques
  • Maurini Corrado
  • Vidoli Stefano
  International Journal of Mechanical Sciences, Elsevier, 2017. Plasticity and damage are two fundamental phenomena in nonlinear solid mechanics associated to the development of inelastic deformations and the reduction of the material stiffness. Alessi et al. [4] have recently shown, through a variational framework, that coupling a gradient-damage model with plasticity can lead to macroscopic behaviours assimilable to ductile and cohesive fracture. Here, we further expand this approach considering specific constitutive functions frequently used in phase-field models of brittle fracture. A numerical solution technique of the coupled elasto-damage-plasticity problem, based on an alternate minimisation algorithm, is proposed and tested against semi-analytical results. Considering a one-dimensional traction test, we illustrate the properties of four different regimes obtained by a suitable tuning of few key constitutive parameters. Namely, depending on the relative yield stresses and softening behaviours of the plasticity and the damage criteria, we obtain macroscopic responses assimilable to (i) brittle fracturèfracturè a la Griffith, (ii) cohesive fractures of the Barenblatt or Dugdale type, and (iii) a sort of cohesive fracture including a depinning energy contribution. The comparisons between numerical and analytical results prove the accuracy of the proposed numerical approaches in the considered quasi-static time-discrete setting, but they also emphasise some subtle issues occurring during time-discontinuous evolutions. (10.1016/j.ijmecsci.2017.05.047)
  DOI : 10.1016/j.ijmecsci.2017.05.047
• Coupling schemes for the FSI forward prediction challenge: comparative study and validation
  
  • Landajuela Mikel
  • Vidrascu Marina
  • Chapelle Dominique
  • Fernández Miguel Angel
  International Journal for Numerical Methods in Biomedical Engineering, John Wiley and Sons, 2017, 33 (4), pp.e02813. This paper presents a numerical study in which several partitioned solution procedures for incompressible fluid-structure interaction are compared and validated against the results of an experimental FSI benchmark. The numerical methods discussed cover the three main families of coupling schemes: strongly coupled, semi-implicit and loosely coupled. Very good agreement is observed between the numerical and experimental results. The comparisons confirm that strong coupling can be efficiently avoided, via semi-implicit and loosely coupled schemes, without compromising stability and accuracy. (10.1002/cnm.2813)
  DOI : 10.1002/cnm.2813
• Imposed curvature of an elastic-plastic strip: application to simulation of coils
  
  • Weisz-Patrault Daniel
  • Ehrlacher Alain
  Mechanics & Industry, EDP Sciences, 2017, 18 (2). – This work is part of the framework of a fast modeling of winding aiming at improving knowledge of residual stress evolution in steel strips and therefore their flatness during the coiling process. An exact analytical solution of an elastic-plastic strip with isotropic hardening at finite strains under an imposed transformation of curvature is developed. Issues related to flow rules for non-differentiable yield functions (Tresca) have been broached and a unique solution is obtained. The equivalence for this transformation, between von Mises and Tresca yield functions is demonstrated. This solution contributes to an efficient model by terms of computation times that aims at simulating coiling by taking into account inelastic deformations and enabling parametric studies in order to improve the process. (10.1051/meca/2016038)
  DOI : 10.1051/meca/2016038
• Caractérisation et modélisation de l'alliage Ti-6Al-4V sous chargement dynamique complexe
  
  • Sotto M. Ruiz De
  • Longère Patrice
  • Doquet V.
  • Papasidero J.
  , 2017.
• Boundary integral equation methods for elastic and plastic problems
  
  • Bonnet Marc
  , 2017, pp.719-749. This chapter deals with formulations based on boundary integral equations (BIEs) for elastic and plastic problems. After a brief review of the basic integral identities of solid mechanics and issues associated with the singular character of the fundamental solutions, the collocation and symmetric Galerkin BIE formulations and the associated boundary element methods (BEMs) are presented in their conventional form where the complete matrix equation is set up using numerical integration and stored. This approach being inadequate for large problem sizes, fast solution techniques are then reviewed, with emphasis on the fast multipole method. Next, BEMs in both collocation and symmetric Galerkin form are described for fracture mechanics and small-strain elastoplasticity. The treatment of the hypersingular integrals arising in the integral representation of tractions on the crack surface or of strains at potentially plastic interior points is discussed, along with other issues. Shape sensitivity analysis techniques are also presented, based on either the direct differentiation of the primary elastic BIE or an adjoint solution. Finally, the symmetric Galerkin BIE is used to define a symmetric formulation for BEM–FEM coupling. (10.1002/9781119176817.ecm2047)
  DOI : 10.1002/9781119176817.ecm2047
• Quasi-static Evolution, Variational Principles and Implicit Scheme in Gradient Plasticity
  
  • Nguyen Quoc-Son
  , 2017, 8, pp.143-152. This paper is devoted to the theory of gradient plasticity. Our attention is focussed on the description of the constitutive equations, on the formulation of the governing equations in terms of the energy potential and the dissipation potential of the solid. The evolution equation is discussed for quasi-static responses. A time-discretization by the implicit scheme of the evolution equation leads to the study of the incremental problem which is different from the rate problem. The incremental problem and associated incremental variational principles are discussed in relation with some existing results of the literature. (10.1007/978-3-319-48884-4_7)
  DOI : 10.1007/978-3-319-48884-4_7
• A novel microstructural interpretation for the biomechanics of mouse skin derived from multiscale characterization
  
  • Lynch Barbara
  • Bancelin Stéphane
  • Bonod-Bidaud Christelle
  • Gueusquin Jean-Baptiste
  • Ruggiero Florence
  • Schanne-Klein Marie-Claire
  • Allain Jean-Marc
  Acta Biomaterialia, Elsevier, 2017, 50, pp.302-311. Skin is a complex, multi-layered organ, with important functions in the protection of the body. The der-mis provides structural support to the epidermal barrier, and thus has attracted a large number of mechanical studies. As the dermis is made of a mixture of stiff fibres embedded in a soft non-fibrillar matrix, it is classically considered that its mechanical response is based on an initial alignment of the fibres, followed by the stretching of the aligned fibres. Using a recently developed setup combining mul-tiphoton microscopy with mechanical assay, we imaged the fibres network evolution during dermis stretching. These observations, combined with a wide set of mechanical tests, allowed us to challenge the classical microstructural interpretation of the mechanical properties of the dermis: we observed a continuous alignment of the collagen fibres along the stretching. All our results can be explained if each fibre contributes by a given stress to the global response. This plastic response is likely due to inner sliding inside each fibre. The non-linear mechanical response is due to structural effects of the fibres network in interaction with the surrounding non-linear matrix. This multiscale interpretation explains our results on genetically-modified mice with a simple alteration of the dermis microstructure. Statement of Significance: Soft tissues, as skin, tendon or aorta, are made of extra-cellular matrix, with very few cells embedded inside. The matrix is a mixture of water and biomolecules, which include the collagen fibre network. The role of the collagen is fundamental since the network is supposed to control the tissue mechanical properties and remodeling: the cells attach to the collagen fibres and feel the network deformations. This paper challenges the classical link between fibres organization and mechanical properties. To do so, it uses multiscale observations combined to a large set of mechanical loading. It thus appears that the behaviour at low stretches is mostly controlled by the network structural response, while, at large stretches, the fibre inner-sliding dominate. (10.1016/j.actbio.2016.12.051)
  DOI : 10.1016/j.actbio.2016.12.051
• Quantitative calorimetric analysis of the fretting damage: Construction of the elastic shakedown boundary
  
  • Moustafa Abdel-Rahman
  • Berthel Bruno
  • Fouvry Siegfried
  • Charkaluk Eric
  International Journal of Fatigue, Elsevier, 2017, 95, pp.143-155. The paper aims to illustrate the relevant use of infrared thermography and energy based approaches to study the plastic behavior and the crack initiation under plain fretting loadings. A well known 35Ni Cr Mo 16 low-alloyed steel was studied under various plain fretting partial slip conditions. The experimental results showed that the proposed 2D image processing method is able to estimate thermoelastic amplitude fields in a good agreement with the theory of linear thermoelasticity, and mean intrinsic dissipation per cycle fields reflecting localized microplastic deformation. The maximal local evolution of the intrinsic dissipation as function of the shear stress amplitude, underlined the presence of a non-dissipative regime, where the specimen mainly undergoes elastic deformation and a dissipative regime where plastic deformation take place. The transition between these two regimes was then coupled with the local elastic shakedown boundary. (10.1016/j.ijfatigue.2016.10.018)
  DOI : 10.1016/j.ijfatigue.2016.10.018
• Dispositif cardiaque
  
  • Chabiniok Radomir
  • Chapelle Dominique
  • Le Gall Arthur
  • Moireau Philippe
  • Vallée Fabrice
  , 2017.
• FR 1753131 - Capteurs chimiques à base de nanotubes de carbone fonctionnalisés par des polymères conjugués pour l'analyse en milieu aqueux
  
  • Zucchi Gaël
  • Lebental Bérengère
  • Loisel Loic
  • Ramachandran Sasikumar
  • Flores Guttierez Alfredo
  • Wang Xin Yang
  • Godumala Mallesham
  • Bodelot Laurence
  , 2017, pp.42p. La présente invention concerne la détection, l'identification et la quantification sélective d'espèces chimiques ioniques dans un fluide, typiquement en phase aqueuse. La présente invention concerne plus particulièrement un capteur chimique miniature destiné notamment à l'analyse de solutions aqueuses. Le capteur comprend des nanotubes de carbone fonctionnalisés en surface par des polymères conjugués porteurs de groupements chimiques appropriés et permettant une telle détection, identification et quantification. Le procédé de préparation et les utilisations du capteur sont décrits.
• Energetic approach for a sliding inclusion accounting for plastic dissipation at the interface, application to phase nucleation
  
  • Bluthé Joffrey
  • Weisz-Patrault Daniel
  • Ehrlacher Alain
  International Journal of Solids and Structures, Elsevier, 2017, 121, pp.163-173. The energy gained at the atomic scale by modifying the crystal lattice during phase nu-cleation is an important aspect to study solid-solid phase transitions. However at the scale of continuum mechanics, the eigenstrain introduced by the geometrical transformation in the newly formed phase is also a significant issue. Indeed, it is responsible for very large elastic energy and dissipation that have to be added to the total energy in order to determine if a phase transition can occur. The eigenstrain can cause sliding of the newly formed grain. In this paper, an analytical solution coupled with numerical energetic optimization is derived to solve the problem of a two-dimensional circular elastic sliding inclusion authorizing plastic dissipation at the interface. Numerical calculations under plane stress assumption show that dissipation enables an effective decrease in the energy needed for the phase transformation to occur. The solution is validated with a comparison with a Finite Element simulation. (10.1016/j.ijsolstr.2017.05.023)
  DOI : 10.1016/j.ijsolstr.2017.05.023
• Caractérisation et modélisation de la rupture de l’alliage Ti-6Al-4V sous chargement dynamique complexe
  
  • Ruiz de Sotto M.
  • Longère Patrice
  • Doquet V.
  • Papasidero J.
  , 2017. no abstract
• Coupled heat conduction and multiphase change problem accounting for thermal contact resistance
  
  • Weisz-Patrault Daniel
  International Journal of Heat and Mass Transfer, Elsevier, 2017, 104, pp.595-606. In this paper, heat conduction coupled with multiphase changes are considered in a cylindrical multilayer composite accounting for thermal contact resistance depending on contact pressures and roughness parameters. A numerical simulation is proposed using both analytical developments and numerical computations. The presented modeling strategy relies on an algorithm that alternates between heat conduction accounting for volumetric heat sources and a multi-phase change model based on non-isothermal Avrami's equation using the isokinetic assumption. Applications to coiling process (winding of a steel strip on itself) are considered. Indeed, phase changes determine the microstructure of the final material and are responsible for residual stresses that create flatness defects. A Finite Element modeling is used for validating the presented solution and numerical results are presented and discussed. (10.1016/j.ijheatmasstransfer.2016.08.091)
  DOI : 10.1016/j.ijheatmasstransfer.2016.08.091
• A homogenization model for porous ductile solids under cyclic loads comprising a matrix with isotropic and linear kinematic hardening
  
  • Cheng Long
  • Danas Kostas
  • Constantinescu Andrei
  • Kondo Djimedo
  International Journal of Solids and Structures, Elsevier, 2017, 121, pp.174-190. In this work, we propose an semi-analytical micromechanical model to study the elasto-plastic response of porous materials subjected to cyclic loading with isotropic and linear kinematic hardening at finite strains. To this end, we use an approximate but numerically efficient decoupled homogenization strategy between the elastic and plastic parts. The resulting effective back stress in the porous solid, similar to the macroscopic stress and plastic strain, has non-zero hydrostatic terms and depends on the porosity, the void shape and orientation as a result of the homogenization process. Subsequently, a complete set of equations is defined to describe the evolution of the microstructure, i.e., void volume fraction (porosity), (ellipsoidal) void shape and orientation both in the elastic and the plastic regimes. The model is then numerically implemented in a general purpose user-material subroutine. Full field finite element simulations of multi-void periodic unit cells are used to assess the predictions of the proposed model. The latter is found to be in good qualitative and quantitative agreement with the finite element results for most of the loading types, hardening parameters and porosities considered in this study, but is less accurate for very small porosities. The combined analytical and numerical study shows that elasticity is an important mechanism for porosity ratcheting in addition to strain hardening. Specifically, in order to recover the main qualitative features of porosity ratcheting for all cyclic loads considered in the present study, it is shown to be critical to take into account the evolution of the microstructure not only during the plastic loading, as is the usual hypothesis, but also during elastic loading. Finally, the effect of isotropic and linear kinematic hardening is found to be highly non-monotonic and non-trivial upon porosity ratcheting for most cases considered here. (10.1016/j.ijsolstr.2017.05.024)
  DOI : 10.1016/j.ijsolstr.2017.05.024
• Light scattering by periodic rough surfaces: equivalent jump conditions
  
  • Gallas Bruno
  • Maurel Agnes
  • Marigo Jean-Jacques
  • Ourir Abdelwaheb
  Journal of the Optical Society of America. A Optics, Image Science, and Vision, Optical Society of America, 2017, 34 (12), pp.2181-2188. We present an interface model based on two-scale homogenization to predict the coherent scattering of light by a periodic rough interface between air and a dielectric. Contrary to previous approaches where the roughnesses are replaced by a layer filled with an equivalent medium, our modeling yields effective jump conditions applying across the region containing the roughnesses. The validity of the model is inspected by comparison with direct numerics and with experimental measurements on a air/silicium rough interface near the Brewster angle. It is shown that the interface model reproduces accurately the shift in the Brewster phenomenon without any ajustable parameter, which is of practical importance in retrieval methods to get thickness or filling fraction with reliable physical values. (10.1364/JOSAA.34.002181)
  DOI : 10.1364/JOSAA.34.002181
• Non-smooth dynamics for an efficient simulation of the grand piano action
  
  • Thorin Anders
  • Boutillon Xavier
  • Lozada José
  • Merlhiot Xavier
  Meccanica, Springer Verlag, 2017, pp.1 - 18. Models with impact or dry friction, yielding discontinuous velocities or accelerations, have motivated research for appropriate numerical methods in the community of non-smooth dynamics. In this work, we apply such methods on the grand piano action. This multibody system has two properties of interest in terms of modelling and simulation: it is extremely sensitive to small misadjustements, and its functioning strongly relies on dry friction and stick-slip transitions—known to be crucial for the touch of the pianist. Using numerical methods of non-smooth contact dynamics, the non-smooth character of dry friction was conserved, in contrast to classical approaches based on regularization which additionally impose the somewhat arbitrary choice of a regularizing parameter. The use of such numerical method resulted in computations about a few hundred times faster than those reported in recent literature. For the first time, the presented predictions of the piano action's simulations are forces (in particular, the reaction force of the key on the pianist's finger), instead of displacements which filter out most of the dynamical subtleties of the mechanism. The comparisons between measured and simulated forces in response to a given motion are successful, which constitutes an excellent validation of the model, from the dynamical and the haptic points of view. Altogether, numerical methods for non-smooth contact dynamics applied to a non-smooth model of the piano action proved to be both accurate and efficient, opening doors to industrial and haptic applications of sensitive multibody systems for which dry friction is essential. <b>Simulation-based videos</b> <ul> <li> Simulations of a keystroke: Your browser does not support the video tag. </li><li> Comparisons between simulations and experiments: Your browser does not support the video tag. </li></ul> <b>Experimental and educational videos</b> <ul> <li> High-speed captures of the piano key mechanism (Left: <i>piano</i> keystroke. Right: <i>forte</i> keystroke.) [A. Thorin and X. Boutillon, LMS@École polytechnique / CEA LIST] Your browser does not support the video tag. Your browser does not support the video tag. </li><li> Explanations on how the mechanism works [A. Thorin based on <a href="https://upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Fortepian_-_mechanizm_angielski.svg/2000px-Fortepian_-_mechanizm_angielski.svg.png"> O. Remez's drawing</a>] Your browser does not support the video tag. </li><li> Tracking of the kinematics using <a href="https://github.com/julien-diener/CRtoolbox"> J. Diener's implementation</a> of KLT tracking algorithms: Your browser does not support the video tag. </li></ul> (10.1007/s11012-017-0641-1)
  DOI : 10.1007/s11012-017-0641-1
• Revisiting the anisotropy of metamaterials for water waves
  
  • Maurel A.
  • Marigo J.-J
  • Cobelli P.
  • Petitjeans P.
  • Pagneux V.
  Physical Review B: Condensed Matter and Materials Physics (1998-2015), American Physical Society, 2017, 96 (13), pp.134310. We establish, both theoretically and experimentally, that metamaterials for water waves reach a much higher degree of anisotropy than the one predicted using the analogy between water waves and their electromagnetic or acoustic counterparts. This is due to the fact that this analogy, based on the two-dimensional shallow water approximation, is unable to account for the three-dimensional near field effects in the water depth. To properly capture these effects, we homogenize the fully three-dimensional problem and show that a subwavelength layered structuration of the bathymetry produces significant anisotropic parameters in the shallow water regime. Furthermore, we extend the validity of the homogenized prediction by proposing an empirical anisotropic version of the dispersion relation. (10.1103/PhysRevB.96.134310)
  DOI : 10.1103/PhysRevB.96.134310
• A peak detection method for identifying phase in physiological signals
  
  • Mitrou Nicholas
  • Laurin Alexandre
  • Dick Taylor
  • Inskip Jessica
  Biomedical Signal Processing and Control, Elsevier, 2017, 31, pp.452 - 462. Introduction To understand the integrated behavior of biological systems, the interactions between their constituent parts are often studied. For example, the interaction between blood pressure and heart rate reveals information about the cardiac baroreflex. For the purpose of characterizing relationships between physiological signals, it is useful to identify phase either as a primary outcome or as an intermediate step to obtain other relevant secondary indices. Existing methods for phase estimation in physiological signals often suffer from a lack of thorough description and standardization, which renders reproducibility and interpretation difficult. A relatively simpler peak detection algorithm was compared to the gold standards of wavelet and Hilbert transforms for its ability to obtain phase. Methods The accuracy and computation time of the peak detection algorithm was compared to the gold standard methods in silico by applying all three to data of known phase, and signal-to-noise ratios from −20 to 5 dB. We then compared the performance of the peak detection method to the Hilbert and wavelet methods by applying each to four different types of in vivo data. Results The peak detection technique is less susceptible to noise and over 10 times faster, computationally, than the wavelet technique. Application to in vivo physiological data shows that equivalent results are obtained from each technique. Conclusions The peak detection method can be used to obtain phase in physiological signals, provide a clearer and more direct interpretation, and be more easily reproducible. Because of its design features, peak detection could also be used to identify individual oscillations in relevant signals, as well as to obtain amplitudes and direct time delays. (10.1016/j.bspc.2016.07.001)
  DOI : 10.1016/j.bspc.2016.07.001
• Bilayer Liquid Crystal and Freedericksz Instability
  
  • Haldar Krishnendu
  • Danas Kostas
  • Triantafyllidis Nicolas
  , 2017. Micro Abstract Liquid crystals are best known for their extensive applications, among many others, in flat display technology. The underlying mechanism is an electro-mechanical coupled phenomenon, followed by an electric field driven instability. This is also known as Freedericksz Transition (FT), where the system evolves with a new stable bifurcated configuration. In this work, through a mixed analytical/numerical study, we present the strong influences of bilayer structure and material constants on the FT.
• A robust and efficient radial return algorithm based on incremental energy minimization for the 3D Souza-Auricchio model for shape memory alloys
  
  • Scalet Giulia
  • Peigney Michaël
  European Journal of Mechanics - A/Solids, Elsevier, 2017, 61, pp.364 - 382. The present paper focuses on the numerical simulation of quasi-static problems involving shape memory alloy (SMA) structures or components. Phe-nomenological constitutive models formulated within the continuum ther-modynamics with internal variable framework describe phase transformation in a SMA by introducing a suitable set of internal variables, which may be constrained to satisfy a set of inequalities. The numerical treatment of such constraints, together with the presence of non-smooth functions and/or complementary conditions in the model formulation, is not an easy task and strongly influences the numerical convergence, algorithm robustness, and computational times. The aim of this paper is to propose a novel state-update procedure for the three-dimensional phenomenological model known as the Souza-Auricchio model. The proposed radial return algorithm, relying on an incremental energy minimization approach, allows for an easy implementation of model equations and internal constraints and avoids the use of regularization parameters for the treatment of non-smooth functions. Several numerical simulations assess the noticeable efficiency, robustness, and performance of the proposed approach, while comparisons with a classical algorithm proposed in the literature show the reduced computational times. (10.1016/j.euromechsol.2016.10.013)
  DOI : 10.1016/j.euromechsol.2016.10.013
• Affine kinematics in planar fibrous connective tissues: an experimental investigation
  
  • Jayyosi Charles
  • Affagard Jean-Sébastien
  • Ducourthial Guillaume
  • Bonod-Bidaud Christelle
  • Lynch Barbara
  • Bancelin Stéphane
  • Ruggiero Florence
  • Schanne-Klein Marie-Claire
  • Allain Jean-Marc
  • Bruyère-Garnier Karine
  • Coret Michel
  Biomechanics and Modeling in Mechanobiology, Springer Verlag, 2017, pp.1–15. The affine transformation hypothesis is usually adopted in order to link the tissue scale with the fibers scale in structural constitutive models of fibrous tissues. Thanks to the recent advances in imaging techniques, such as multiphoton microscopy, the microstructural behavior and kinematics of fibrous tissues can now be monitored at different stretching within the same sample. Therefore, the validity of the affine hypothesis can be investigated. In this paper, the fiber reorientation predicted by the affine assumption is compared to experimental data obtained during mechanical tests on skin and liver capsule coupled with microstructural imaging using multiphoton microscopy. The values of local strains and the collagen fibers orientation measured at increasing loading levels are used to compute a theoretical estimation of the affine reorientation of collagen fibers. The experimentally measured reorientation of collagen fibers during loading could not be successfully reproduced with this simple affine model. It suggests that other phenomena occur in the stretching process of planar fibrous connective tissues, which should be included in structural constitutive modeling approaches. (10.1007/s10237-017-0899-1)
  DOI : 10.1007/s10237-017-0899-1
• Two scale homogenization of a row of locally resonant inclusions - the case of anti-plane shear waves
  
  • Pham Kim
  • Maurel Agnes
  • Marigo Jean-Jacques
  Journal of the Mechanics and Physics of Solids, Elsevier, 2017, 106, pp.80-94. We present a homogenization model for a single row of locally resonant inclusions. The resonances , of the Mie type, result from a high contrast in the shear modulus between the inclusions and the elastic matrix. The presented homogenization model is based on a matched asymptotic expansion technique; it slightly di↵ers from the classical homogenization which applies for thick arrays with many rows of inclusions (and thick means large compared to the wavelength in the matrix). Instead of the effective bulk parameters found in the classical homogenization, we end up with interface parameters entering in jump conditions for the displacement and for the normal stress; among these parameters, one is frequency dependent and encapsulates the resonant behavior of the inclusions. Our homogenized model is validated by comparison with results of full wave calculations. It is shown to be ecient in the low frequency domain and accurately describes the e↵ects of the losses in the soft inclusions. (10.1016/j.jmps.2017.05.001)
  DOI : 10.1016/j.jmps.2017.05.001
• Effective Dynamic Properties of a Row of Elastic Inclusions: The Case of Scalar Shear Waves
  
  • Marigo Jean-Jacques
  • Maurel Agnes
  • Pham Kim
  • Sbitti Amine
  Journal of Elasticity, Springer Verlag, 2017, 128 (2), pp.265-289. We present the homogenization of a periodic array of elastic inclusions embedded in an elastic matrix. We consider shear elastic waves with a typical wavelength 1/k much larger than the array spacing h and thickness e. Owing to the small parameter η = kh, with e/h = O(1), a matched asympto-tic expansion technique is applied to the wave equation in the time domain. The homogenized problem involves an equivalent interface associated to jump conditions of the Ventcels type. Up to the accuracy of the model in O(η2), different jump conditions are possible, which correspond to enlarged versions of the interface ; these jump conditions are parametrized by the thickness a of the homogenized interface. We inspect the influence of a (i) on the equation of energy conservation in the homogenized problem and (ii) on the error of the model for a simple scattering problem. We show that restoring the thickness of the real array, a = e, is the optimal configuration regarding both aspects. (10.1007/s10659-017-9627-4)
  DOI : 10.1007/s10659-017-9627-4
• Two-field surface pattern control via marginally stable magnetorheological elastomers
  
  • Psarra Erato
  • Bodelot Laurence
  • Danas Kostas
  Soft Matter, Royal Society of Chemistry, 2017, 13 (37), pp.6576 - 6584. The stability and post-bifurcation of a non-linear magnetoelastic film/substrate block is experimentally exploited to obtain active control of surface roughness. The non-intuitive interplay between magnetic field and elastic deformation owes to material and geometry selection, namely a ferromagnetic particle composite film bonded on a compliant passive foundation. Cooperation of two otherwise independent loading mechanisms–mechanical pre-compression and magnetic field–allows to bring the structure near a marginally stable state and then destabilize it with either magnetic or mechanical fields. We demonstrate for the first time that the critical magnetic field is a decreasing function of pre-compression and vice versa. The experimental results are then probed successfully with full-field finite element simulations at large strains and magnetic fields. The magnetoelastic coupling allows for the reversible on/off control of surface wrinkling under adjustable critical magnetic and mechanical fields, thus this study constitutes a first step towards realistic active haptic and morphing devices. (10.1039/C7SM00996H)
  DOI : 10.1039/C7SM00996H