Publications

2015

• Fourth order energy-preserving locally implicit time discretization for linear wave equations
  
  • Chabassier Juliette
  • Imperiale Sébastien
  International Journal for Numerical Methods in Engineering, Wiley, 2015. A family of fourth order coupled implicit-explicit time schemes is presented as a special case of fourth order coupled implicit schemes for linear wave equations. The domain of interest is decomposed into several regions where different fourth order time discretization are used, chosen among a family of implicit or explicit fourth order schemes. The coupling is based on a Lagrangian formulation on the boundaries between the several non conforming meshes of the regions. A global discrete energy is shown to be preserved and leads to global fourth order consistency in time. Numerical results in 1d and 2d for the acoustic and elastodynamics equations illustrate the good behavior of the schemes and their potential for the simulation of realistic highly heterogeneous media or strongly refined geometries, for which using everywhere an explicit scheme can be extremely penalizing. Accuracy up to fourth order reduces the numerical dispersion inherent to implicit methods used with a large time step, and makes this family of schemes attractive compared to second order accurate methods. (10.1002/nme.5130)
  DOI : 10.1002/nme.5130
• Displacement Reconstructions in Ultrasound Elastography
  
  • Bal Guillaume
  • Imperiale Sébastien
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2015, 8 (2), pp.1070-1089. We consider the reconstruction of internal elastic displacements from ultrasound measurements , which finds applications in the medical imaging modality called elastography. By appropriate interferometry and windowed Fourier transforms of the ultrasound measurements, we propose a reconstruction procedure of the vectorial structure of spatially varying elastic displacements in biological tissues. This provides a modeling and generalization of scalar reconstruction procedures routinely used in elastography. The proposed algorithm is justified using a single scattering approximation and local asymptotic analysis. Its validity is assessed by numerical simulations. (10.1137/140988504)
  DOI : 10.1137/140988504
• Numerical investigation on corner singularities in cracked plates using the G-theta method with an adapted theta field
  
  • Vu Minh Ngoc
  • Geniaut Samuel
  • Massin Patrick
  • Marigo Jean-Jacques
  Theoretical and Applied Fracture Mechanics, Elsevier, 2015, 77, pp.59-68. G-theta method with appropriate virtual crack extension (theta field) is proposed for the accurate evaluation of energy release rate along a crack edge which is non-orthogonal to the free surface. This method is implemented in the framework of finite element procedure as well as extended finite element one. This numerical procedure is then applied to investigate the corner singularities in cracked plates. The superposition of numerical solution to asymptotic solution within the boundary layer of crack front allows showing the dependence of vertex singularity to plate thickness. (10.1016/j.tafmec.2015.02.003)
  DOI : 10.1016/j.tafmec.2015.02.003
• Highly reproducible, hysteresis-free, flexible strain sensors by inkjet printing of carbon nanotubes
  
  • Michelis Fulvio
  • Bodelot Laurence
  • Bonnassieux Yvan
  • Lebental Bérengère
  Carbon, Elsevier, 2015, 95, pp.pp 1020-1026. In order to build upon the exceptional interest for flexible sensors based on carbon nanotube networks (CNNs), the field requires high device-to-device reproducibility. Inkjet printing has provided outstanding results for flexible ohmic sensors in terms of reproducibility of their resistance. However, the reproducibility of the sensitivity, the most critical parameter for sensing application, has been only marginally assessed. In the present paper, CNN based resistive strain sensors fabricated by inkjet-printing on flexible Ethylene Tetrafluoroethylene (EFTE) sheets are presented. The variability on the device initial resistance is studied for 5 different batches of sensors from 3 to 72 devices each. The variability ranges between 8.4% and 43% depending on the size of the batches, with a 20% average. An 8-device batch with 15% variability on initial resistance is further studied for variability on the strain and thermal sensitivity. Standard deviation values are found to be as low as 16% on the strain sensitivity and 8% on the temperature sensitivity. Moreover, the devices are hysteresis free, a rare achievement for CNT strain sensors on plastics. (10.1016/j.carbon.2015.08.103)
  DOI : 10.1016/j.carbon.2015.08.103
• Mechanics of collective unfolding
  
  • Caruel Matthieu
  • Allain Jean-Marc
  • Truskinovsky Lev
  Journal of the Mechanics and Physics of Solids, Elsevier, 2015, 76, pp.237 - 259. Mechanically induced unfolding of passive crosslinkers is a fundamental biological phenomenon encountered across the scales from individual macro-molecules to cytoskeletal actin networks. In this paper we study a conceptual model of athermal load-induced unfolding and use a minimalistic setting allowing one to emphasize the role of long-range interactions while maintaining full analytical transparency. Our model can be viewed as a description of a parallel bundle of N bistable units confined between two shared rigid backbones that are loaded through a series spring. We show that the ground states in this model correspond to synchronized, single phase configurations where all individual units are either folded or unfolded. We then study the fine structure of the wiggly energy landscape along the reaction coordinate linking the two coherent states and describing the optimal mechanism of cooperative unfolding. Quite remarkably, our study shows the fundamental difference in the size and structure of the folding-unfolding energy barriers in the hard (fixed displacements) and soft (fixed forces) loading devices which persists in the continuum limit. We argue that both, the synchronization and the non-equivalence of the mechanical responses in hard and soft devices, have their origin in the dominance of long-range interactions. We then apply our minimal model to skeletal muscles where the power-stroke in acto-myosin crossbridges can be interpreted as passive folding. A quantitative analysis of the muscle model shows that the relative rigidity of myosin backbone provides the long-range interaction mechanism allowing the system to effectively synchronize the power-stroke in individual crossbridges even in the presence of thermal fluctuations. In view of the prototypical nature of the proposed model, our general conclusions pertain to a variety of other biological systems where elastic interactions are mediated by effective backbones. (10.1016/j.jmps.2014.11.010)
  DOI : 10.1016/j.jmps.2014.11.010
• Dynamics of a spherical capsule in a planar hyperbolic flow: influence of bending resistance
  
  • Dupont Claire
  • Le Tallec P
  • Barthes-Biesel Dominique
  • Vidrascu Marina
  • Salsac A.-V
  , 2015, 16. We consider an initially spherical capsule freely suspended in a planar hyperbolic flow and study the influence of the wall bending resistance on the capsule dynamics. The capsule wall is assumed to be made of a three-dimensional homogeneous elastic material. The fluid-structure interaction between the capsule and the external flow is modeled numerically by coupling a boundary integral method with a shell finite element method. It is found that, for given three-dimensional wall mechanical properties, the capsule deformability is drastically reduced as the bending resistance is increased. But, if one expresses the same results as a function of the two-dimensional mechanical properties of the mid-surface, which is how the capsule wall is modeled in the thin-shell model, the capsule deformed shape is identical to the one predicted for a capsule devoid of bending resistance. The bending rigidity is found to have a negligible influence on the shape and deformation: the capsule main deformation mode is thus solely a function of the elastic stretching of the mid-surface. The wall bending resistance still plays a role locally in the regions where buckling occurs. Its influence is studied in the low flow strength regime, for which wrinkling of the wall is observed to persist at steady state. We show that the wrinkle wavelength only depends on the bending number, which compares the relative importance of bending and shearing phenomena, and provide the correlation law. This result is interesting as it allows bending resistance to be estimated from experiments on capsules in a planar hyperbolic flow at low flow strength. (10.1016/j.piutam.2015.03.009)
  DOI : 10.1016/j.piutam.2015.03.009
• Reconstruction of a constitutive law for rubber from in silico experiments using Ogden's laws
  
  • de Buhan Maya
  • Gloria Antoine
  • Le Tallec Patrick
  • Vidrascu Marina
  International Journal of Solids and Structures, Elsevier, 2015, pp.16. This article deals with the following data assimilation problem: construct an analytical approximation of a numerical constitutive law in three-dimensional nonlinear elasticity. More precisely we are concerned with a micro-macro model for rubber. Macroscopic quantities of interest such as the Piola-Kirchhoff stress tensor can be approximated for any value of the strain gradient by numerically solving a nonlinear PDE. This procedure is however computationally demanding. Hence, although conceptually satisfactory, this physically-based model is of no direct practical use. The aim of this article is to circumvent this difficulty by proposing a numerical strategy to reconstruct from in silico experiments an accurate analytical proxy for the micro-macro constitutive law. (10.1016/j.ijsolstr.2015.02.026)
  DOI : 10.1016/j.ijsolstr.2015.02.026