Publications

2017

• Mathematical and numerical modeling of plate dynamics with rotational inertia
  
  • Bonaldi Francesco
  • Geymonat Giuseppe
  • Krasucki Françoise
  • Vidrascu Marina
  Journal of Numerical Mathematics, De Gruyter, 2017, 26 (1), pp.1 - 20. We give a presentation of the mathematical and numerical treatment of plate dynamics problems including rotational inertia. The presence of rotational inertia in the equation of motion makes the study of such problems interesting. We employ HCT finite elements for space discretization and the Newmark method for time discretization in FreeFEM++, and test such methods in some significant cases: a circular plate clamped all over its lateral surface, a rectangular plate simply supported all over its lateral surface, and an L-shaped clamped plate. (10.1515/jnma-2016-1020)
  DOI : 10.1515/jnma-2016-1020
• Recent advances in studying single bacteria and biofilm mechanics
  
  • Even Catherine
  • Marlière Christian
  • Ghigo Jean-Marc
  • Allain Jean-Marc
  • Marcellan Alba
  • Raspaud Eric
  Advances in Colloid and Interface Science, Elsevier, 2017, pp.57. Bacterial biofilms correspond to surface-associated bacterial communities embedded in hydrogel-like matrix, in which high cell density, reduced diffusion and physico-chemical heterogeneity play a protective role and induce novel behaviors. In this review, we present recent advances on the understanding of how bacterial mechanical properties, from single cell to high-cell density community, determine biofilm tri-dimensional growth and eventual dispersion and we attempt to draw a parallel between these properties and the mechanical properties of other well-studied hydrogels and living systems. (10.1016/j.cis.2017.07.026)
  DOI : 10.1016/j.cis.2017.07.026
• Homogenization of Thin and Thick Metamaterials and Applications
  
  • Ourir Abdelwaheb
  • Gao Yao
  • Maurel Agnès
  • Marigo Jean-Jacques
  , 2017, pp.149-165. The wave propagation in structures involving metamaterials can be described owing to homogenization approaches which allow to replace the material structured at the subwavelength scale by an equivalent and simpler, effective medium. In its simplest form, homogenization predicts that the equivalent medium is homogeneous and aniso-tropic and it is associated to the usual relations of continuity for the electric and magnetic fields at the boundaries of the metamaterial structure. However, such prediction has a range of validity which remains limited to relatively thick devices and it is not adapted to more involved geometries (notably three-dimensional). The following two aspects are considered: (i) we study how the homogenization at the leading order can be improved when the thickness of the device becomes small and (ii) we propose a heuris-tic extension of the solution given by the leading order homogenization in order to deal with a complex geometry; in the latter case, an application to a demultiplexer device is proposed. (10.5772/66035)
  DOI : 10.5772/66035
• Deformation mechanisms of idealised cermets under multi-axial loading
  
  • Bele E.
  • Goel A.
  • Pickering G.
  • Borstnar G.
  • Katsamenis O.L.
  • Pierron F.
  • Danas Kostas
  • Deshpande V.S.
  Journal of the Mechanics and Physics of Solids, Elsevier, 2017, 102, pp.80-100. The response of idealised cermets comprising approximately 60% by volume steel spheres in a Sn/Pb solder matrix is investigated under a range of axisymmetric compressive stress states. Digital volume correlation (DVC) anal`ysis of X-ray micro-computed tomography scans (μ-CT), and the measured macroscopic stress-strain curves of the specimens revealed two deformation mechanisms. At low triaxialities the deformation is granular in nature, with dilation occurring within shear bands. Under higher imposed hydrostatic pressures, the deformation mechanism transitions to a more homogeneous incompressible mode. However, DVC analyses revealed that under all triaxialities there are regions with local dilatory and compaction responses, with the magnitude of dilation and the number of zones wherein dilation occurs decreasing with increasing triaxiality. Two numerical models are presented in order to clarify these mechanisms: (i) a periodic unit cell model comprising nearly rigid spherical particles in a porous metal matrix and (ii) a discrete element model comprising a large random aggregate of spheres connected by non-linear normal and tangential “springs”. The periodic unit cell model captured the measured stress-strain response with reasonable accuracy but under-predicted the observed dilation at the lower triaxialities, because the kinematic constraints imposed by the skeleton of rigid particles were not accurately accounted for in this model. By contrast, the discrete element model captured the kinematics and predicted both the overall levels of dilation and the simultaneous presence of both local compaction and dilatory regions with the specimens. However, the levels of dilation in this model are dependent on the assumed contact law between the spheres. Moreover, since the matrix is not explicitly included in the analysis, this model cannot be used to predict the stress-strain responses. These analyses have revealed that the complete constitutive response of cermets depends both on the kinematic constraints imposed by the particle aggregate skeleton, and the constraints imposed by the metal matrix filling the interstitial spaces in that skeleton. (10.1016/j.jmps.2017.01.002)
  DOI : 10.1016/j.jmps.2017.01.002
• A homogenization model of the Voigt type for skeletal muscle
  
  • Spyrou L.A.
  • Agoras M.
  • Danas Kostas
  Journal of Theoretical Biology, Elsevier, 2017, 414, pp.50-61. A three-dimensional constitutive model for skeletal muscle incorporating microstructural characteristics is developed and numerically implemented in a general purpose finite element program. The proposed model takes into account explicitly the volume fractions of muscle fibers and connective tissue by using the Voigt homogenization approach to bridge the different length scales of the muscle structure. The model is used to estimate the active and passive homogenized muscle response. Next, the model is validated by experimental data and periodic three-dimensional unit cell calculations comprising various fiber volume fractions and mechanical properties of the constituents. The model is found to be in very good agreement with both the experimental data and the finite element results for all the examined cases. The influence of fiber volume fraction and material properties of constituents on effective muscle response under several loading conditions is examined. (10.1016/j.jtbi.2016.11.018)
  DOI : 10.1016/j.jtbi.2016.11.018
• Polarization-resolved Second Harmonic Imaging of collagen organization in connective tissues - Application to biomechanics
  
  • Teulon Claire
  • Latour Gaël
  • Gusachenko Ivan
  • Ducourthial Guillaume
  • Bancelin Stéphane
  • Bonod-Bidaud Christelle
  • Ruggiero Florence
  • Affagard Jean-Sébastien
  • Lynch Barbara
  • Benoit Aurélie
  • Allain Jean-Marc
  • Schanne-Klein Marie-Claire
  , 2017, pp.NW3C.2. Polarization-resolved SHG microscopy enables measurements of the main orientation and the angular dispersion of collagen fibrils within the focal volume. Results are presented in cornea, tendon and skin, eventually as function of mechanical stress. (10.1364/NTM.2017.NW3C.2)
  DOI : 10.1364/NTM.2017.NW3C.2
• An Experimental Technique For The Characterization Of Adhesive Joints Under Dynamic Multiaxial Loadings
  
  • Janin Anthony
  • Constantinescu Andrei
  • Weisz-Patrault Daniel
  • Nevière Robert
  • Stackler Matthieu
  • Albouy William
  Procedia Engineering, Elsevier, 2017, 197, pp.52-59. This paper deals with experimental testing of adhesive joints, whose characterization under static loadings drove a large number of studies and techniques. However, few studies deal with dynamic loadings and most of them are limited to the characterization of the shear strength of the bonded assembly. Indeed, dynamic tests often rely on single or double-lap joint specimens that do not enable to investigate multiaxial loadings. This paper is dedicated to the development of an innovative experimental technique for the characterization of adhesive joints under dynamic multiaxial loadings. The experimental apparatus consists in a conventional Split Hopkinson Pressure Bar (SHPB), a newly designed specimen named DODECA and local measurements performed by Digital Image Correlation (DIC). The specimen conception and sizing are detailed with numerical computations as well as preparation procedures. One of the advantages of the proposed specimen is the possibility of testing three distinct multiaxial loadings with the same methodology. This new technique enables to measure strains in adhesive joints accurately with a dynamic loading. (10.1016/j.proeng.2017.08.081)
  DOI : 10.1016/j.proeng.2017.08.081
• Effective and energy-preserving time discretization for a general nonlinear poromechanical formulation
  
  • Burtschell Bruno
  • Chapelle Dominique
  • Moireau Philippe
  Computers & Structures, Elsevier, 2017, 182, pp.313-324. We consider a general nonlinear poromechanical model, formulated based on fundamental thermodynamics principle, suitable for representing the coupling of rapid internal fluid flows with large deformations of the solid, and compatible with a wide class of constitutive behavior. The objective of the present work is to propose for this model a time discretization scheme of the partitioned type, to allow the use of existing time schemes - and possibly separate solvers - for each component of the model, i.e. for the fluid and the solid. To that purpose, we adapt and extend an earlier proposed approach devised for fluid-structure interaction in an Arbitrary Lagrangian-Eulerian framework. We then establish an energy estimate for the resulting time scheme, in a form that is consistent with the underlying energy principle in the poromechanical formulation, up to some numerical dissipation effects and some perturbations that we have carefully identified and assessed. In addition, we provide some numerical illustrations of our numerical strategy with test problems that present typical features of large strains and rapid fluid flows, and also a case of singular transition related to total drainage. An example of challenging application envisioned for this model and associated numerical coupling scheme concerns the perfusion of the heart. (10.1016/j.compstruc.2016.10.022)
  DOI : 10.1016/j.compstruc.2016.10.022
• An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling
  
  • Rausch Manuel K.
  • Genet Martin
  • Humphrey Jay D.
  Journal of Biomechanics, Elsevier, 2017, 58, pp.227 - 231. Continuing advances in computational power and methods have enabled image-based biomechanical modeling to become a crucial tool in basic science, diagnostic and therapeutic medicine, and medical device design. One of the many challenges of this approach, however, is the identification of a stress-free reference configuration based on in vivo images of loaded and often prestressed or residually stressed soft tissues and organs. Fortunately, iterative methods have been proposed to solve this inverse problem, among them Sellier’s method. This method is particularly appealing for it is easy to implement, convergences reasonably fast, and can be coupled to nearly any finite element package. However, by means of several practical examples, we demonstrate that in its original formulation Sellier’s method is not optimally fast and may not converge for problems with large deformations. Fortunately, we can also show that a simple, inexpensive augmentation of Sellier’s method based on Aitken’s delta-squared process can not only ensure convergence but also significantly accelerate the method. (10.1016/j.jbiomech.2017.04.021)
  DOI : 10.1016/j.jbiomech.2017.04.021