Publications

2021

• Model reduction techniques for quantitative nano-mechanical AFM mode
  
  • Chang Xuyang
  • Roux Stéphane
  • Hallais Simon
  • Danas Kostas
  Measurement Science and Technology, IOP Publishing, 2021. A recently developed atomic force microscope (AFM) process, the Peak-Force Quantitative Nanomechanical Mapping (PF-QNM) mode, allows to probe over a large spatial region surface topography together with a variety of mechanical properties (e.g. apparent modulus, adhesion, viscosity). The resulting large set of data often exhibits strong coupling between material response and surface topography. This letter proposes the use of a proper orthogonal decomposition (POD) technique to analyze and segment the force-indentation data obtained by the PF-QNM mode in a highly efficient and robust manner. Two samples illustrate the proposed methodology. In the first one, low density polyethylene nanopods are deposited on a polystyrene film. The second is made of carbonyl iron particles embedded in a polydimethylsiloxane matrix. The proposed POD method permits to seamlessly identify the underlying phase constituents in both samples and decouple them from the surface topography by compressing voluminous force-indentation data into a subset with a much lower dimensionality.
• Coupling of complex function theory and finite element method for crack propagation through energetic formulation: conformal mapping approach and reduction to a Riemann-Hilbert problem
  
  • Legatiuk Dmitrii
  • Weisz-Patrault Daniel
  Computational Methods and Function Theory, Springer, 2021. In this paper we present a theoretical background of a coupled analytical-numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical-numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of the complex function theory and couple it continuously with the finite element solution in the region far from singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann-Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles on the way of practical realisation of this strategy. (10.1007/s40315-021-00403-7)
  DOI : 10.1007/s40315-021-00403-7
• Systematic two-scale image analysis of extreme deformations in soft architectured sheets
  
  • Agnelli Filippo
  • Margerit Pierre
  • Celli Paolo
  • Daraio Chiara
  • Constantinescu Andrei
  International Journal of Mechanical Sciences, Elsevier, 2021, 194, pp.106205. The multi-scale nature of architectured materials raises the need for advanced experimental methods suitable for the identification of their effective properties, especially when their size is finite and they undergo extreme deformations. The present work demonstrates that state-of-the art image processing methods combined with numerical and analytical models provide a comprehensive quantitative description of these solids and their global behaviour, including the influence of the boundary conditions, of the manufacturing process, and of geometric and constitutive non-linearities. To this end, an adapted multi-scale digital image correlation analysis is used to track both elongations and rotations of particular features of the unit cell at the local and global (homogenized) scale of the material. This permits to observe with unprecedented clarity the strain fields for various unit cells in the structure and to detect global deformation patterns and heterogeneities of the homogenized strain distribution. This method is here demonstrated on elastic sheets undergoing extreme longitudinal and shear deformations. These experimental results are compared to non-linear finite element simulations, which are also used to evaluate the effects of manufacturing imperfections on the response. A skeletal representation of the architectured solid is then extracted from the experiments and used to create a purely-kinematic truss-hinge model that can accurately capture its behaviour. The analysis proposed in this work can be extended to guide the design of twodimensional architectured solids featuring other regular, quasi-regular or graded patterns, and subjected to other types of loads. (10.1016/j.ijmecsci.2020.106205)
  DOI : 10.1016/j.ijmecsci.2020.106205
• Experiments and numerical implementation of a boundary value problem involving a magnetorheological elastomer layer subjected to a non-uniform magnetic field
  
  • Dorn Charles
  • Bodelot Laurence
  • Danas Kostas
  Journal of Applied Mechanics, American Society of Mechanical Engineers, 2021, pp.1-12. (10.1115/1.4050534)
  DOI : 10.1115/1.4050534
• Translational Cardiovascular Modeling: Tetralogy of Fallot and Modeling of Diseases
  
  • Chabiniok Radomir
  • Škardová Kateřina
  • Galabov Radek
  • Eichler Pavel
  • Gusseva Maria
  • Janoušek Jan
  • Fučík Radek
  • Tintěra Jaroslav
  • Oberhuber Tomáš
  • Hussain Tarique
  , 2021. Translational cardiovascular modeling (TCM) combines clinical data with physiologically and biophysically based models of the heart, vessels or circulation, while aiming to contribute to diagnosis or optimal clinical management. Models of heart mechanics and electromechanical models are applicable when assessing ventricular function, contributing to planning of optimal intervention. During a pe- rioperative period or acute exacerbation of heart failure, close to real time running models can be coupled with signals monitoring cardiovascular physiology. Blood flow assessed by combining phase contrast magnetic resonance imaging with flow models can contribute to the decision about a possible intervention e.g. on heart valves or large vessels. Furthermore, advanced imaging and image processing con- strained by biophysical models allows for the study of distinct patterns, which could contribute to early detection or mapping a disease progress. In this chapter we demonstrate applicability of some TCM methods on tetralogy of Fallot (TOF) – the most common cyanotic congenital heart disease. A number of already existing modeling techniques can be applied on the cohort of TOF. Likewise, some novel techniques developed specifically for the group of TOF patients could serve in some other pathologies. This whole approach leads to an acronym TOFMOD, standing for Tetralogy of Fallot and Modeling of Diseases.
• A stable, unified model for resonant Faraday cages
  
  • Delourme Bérangère
  • Lunéville Éric
  • Marigo Jean-Jacques
  • Maurel Agnès
  • Mercier Jean-François
  • Pham Kim
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2021, 477 (2245), pp.20200668. We study some effective transmission conditions able to reproduce the effect of a periodic array of Dirichlet wires on wave propagation, in particular when the array delimits an acoustic Faraday cage able to resonate. In the study of Hewett & Hewitt (2016 Proc. R. Soc. A 472 , 20160062 ( doi:10.1098/rspa.2016.0062 )) different transmission conditions emerge from the asymptotic analysis whose validity depends on the frequency, specifically the distance to a resonance frequency of the cage. In practice, dealing with such conditions is difficult, especially if the problem is set in the time domain. In the present study, we demonstrate the validity of a simpler unified model derived in Marigo & Maurel (2016 Proc. R. Soc. A 472 , 20160068 ( doi:10.1098/rspa.2016.0068 )), where unified means valid whatever the distance to the resonance frequencies. The effectiveness of the model is discussed in the harmonic regime owing to explicit solutions. It is also exemplified in the time domain, where a formulation guaranteeing the stability of the numerical scheme has been implemented. (10.1098/rspa.2020.0668)
  DOI : 10.1098/rspa.2020.0668
• Numerical Analysis of a Method for Solving 2D Linear Isotropic Elastodynamics with Free Boundary Condition using Potentials and Finite Elements
  
  • Albella Martínez Jorge
  • Imperiale Sébastien
  • Joly Patrick
  • Rodríguez Jerónimo
  Mathematics of Computation, American Mathematical Society, 2021, 90. When solving 2D linear elastodynamic equations in a homogeneous isotropic media, a Helmholtz decomposition of the displacement field decouples the equations into two scalar wave equations that only interact at the boundary. It is then natural to look for numerical schemes that independently solve the scalar equations and couple the solutions at the boundary. The case of rigid boundary condition was treated In [3, 2]. However in [4] the case of free surface boundary condition was proven to be unstable if a straight- forward approach is used. Then an adequate functional framework as well as a time domain mixed formulation to circumvent these issues was presented. In this work we first review the formulation presented in [4] and propose a subsequent discretised formulation. We provide the complete stability analysis of the corresponding numerical scheme. Numerical results that illustrate the theory are also shown. (10.1090/mcom/3613)
  DOI : 10.1090/mcom/3613
• FIB manufactured microstructures with low Coefficients of Thermal Expansion
  
  • Héripré Eva
  • Mehrez Marwen
  • Constantinescu Andrei
  Mechanics Research Communications, Elsevier, 2021. (10.1016/j.mechrescom.2021.103667)
  DOI : 10.1016/j.mechrescom.2021.103667