Publications

2021

• Asymptotic derivation of high-order rod models from non-linear 3D elasticity
  
  • Audoly Basile
  • Lestringant Claire
  Journal of the Mechanics and Physics of Solids, Elsevier, 2021, 148, pp.104264. We propose a method for deriving equivalent one-dimensional models for slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, finite rotations, arbitrary cross-sections shapes, inhomogeneous elastic properties across the crosssection, arbitrary elastic constitutive laws (possibly with low symmetry) and arbitrary distributions of pre-strain, including finite pre-strain. It is based on a kinematic parameterization of the actual configuration that makes use of a center-line, a frame of directors, and local degrees of freedom capturing the detailed shape of cross-sections. A relaxation method is applied that holds the framed center-line fixed while relaxing the local degrees of freedom; it is asymptotically valid when the macroscopic strain and the properties of the rod vary slowly in the longitudinal direction. The outcome is a one-dimensional strain energy depending on the apparent stretching, bending and twisting strain of the framed center-line; the dependence on the strain gradients is also captured, yielding an equivalent rod model that is asymptotically exact to higher order. The method is presented in a fully non-linear setting and it is verified against linear and weakly non-linear solutions available from the literature.
• Shape-shifting panel from 3D printed undulated ribbon lattice
  
  • Agnelli Filippo
  • Tricarico Michele
  • Constantinescu Andrei
  Extreme Mechanics Letters, Elsevier, 2021, 42, pp.101089. Materials that change their shape in response to external stimuli open up new prospects for efficient and versatile design and shaping of three-dimensional objects. Here, we present a novel class of micro-structures exhibiting an extension-bending coupling (EBC) effect, that can be harnessed as an elementary building block for shape-shifting panels. They are built with a single material as a network of undulated ribbons. The deformations mechanisms of both single and connected undulated ribbons are analysed using the finite element method to explain the main features of the EBC mechanism. For a particular micro-structure of the proposed class, the elastic response is investigated both under small strain assumption combining two-scale homogenization with Kirchhoff-Love plate theory, and at finite strains relying on numerical analysis. The range of achievable EBC ratio is then assessed with respect to the geometric parameters of the unit cell. Patterned specimens are manufactured using a commercial FFF Ultimaker 3D printer and are mechanically tested at finite strain up to 20%. The displacement measured by point tracking match the predictions from the finite element simulations and indicate that the structure maintain its properties at finite strain. Moreover, a tensile test load with point-like boundary is proposed to highlight exceptional out of plane displacement. The proposed ribbon based architectures can be combined with active materials for the actuation of shape shifting structures, like soft robots, control systems and power devices. (10.1016/j.eml.2020.101089)
  DOI : 10.1016/j.eml.2020.101089
• Linear viscoelasticity of an acrylate IPN, analysis and micromechanical modeling
  
  • Diani Julie
  • Strauch-Hausser Éléonore
  Soft Matter, Royal Society of Chemistry, 2021, 17 (31), pp.7341 - 7349. An amorphous acrylate interpenetrated polymer network (IPN) was made in lab and tested by dynamic mechanical analysis. Using frequency sweep tests, it was shown that the time-temperature superposition principle applies to the double network. Moreover, a generalized Maxwell model with forty Maxwell branches successfully reproduced the material linear viscoelasticity. Using temperature sweep tests, the IPN linear viscoelasticity has been estimated by micromechanics, applying both mean-field homogenization models and fast Fourier transform (FFT)-based homogenization techniques. This modeling effort allowed discussing the simple network mechanical interactions. The microstructure of a second network, defined by a self-avoiding random walk, embedded in a continuous medium, in place of the first network, is shown to provide with satisfactory estimates of the IPN linear viscoelasticity. (10.1039/d1sm00808k)
  DOI : 10.1039/d1sm00808k
• Non-oxide precipitates in additively manufactured austenitic stainless steel
  
  • Upadhyay Manas Vijay
  • Ben Haj Slama Meriem
  • Gaudez Steve
  • Mohanan Nikhil
  • Yedra Lluis
  • Hallais Simon
  • Héripré Eva
  • Tanguy Alexandre
  Scientific Reports, Nature Publishing Group, 2021. Precipitates in an austenitic stainless steel fabricated via any Additive Manufacturing (AM), or 3D printing, technique have been widely reported to be only Mn-Si-rich oxides. However, via Transmission Electron Microscopy (TEM) studies on a 316L stainless steel, we show that non-oxide precipitates (intermetallics, sulfides, phosphides and carbides) can also form when the steel is fabricated via Laser Metal Deposition (LMD)-a directed energy deposition-type AM technique. An investigation into their origin is conducted with support from precipitation kinetics and finite element heat transfer simulations. It reveals that non-oxide precipitates form during solidification/cooling at temperatures ≥ 0.75Tm (melting point) and temperature rates ≤ 10 5 K/s, which is the upper end of the maximum rates encountered during LMD but lower than those encountered during Selective Laser Melting (SLM)-a powder-bed type AM technique. Consequently, non-oxide precipitates should form during LMD, as reported in this work, but not during SLM, in consistency with existing literature. (10.1038/s41598-021-89873-2)
  DOI : 10.1038/s41598-021-89873-2
• Perfusion Index: Physical Principles, Physiological Meanings and Clinical Implications in Anaesthesia and Critical Care
  
  • Coutrot Maxime
  • Dudoignon Emmanuel
  • Md Jona Joachim
  • Gayat Etienne
  • Vallee Fabrice
  • Depret François
  Anaesthesia Critical Care & Pain Medicine, Elsevier Masson, 2021. Photoplethysmography (PPG) has been extensively used for pulse oximetry monitoring in anaesthesia, perioperative and intensive care. However, some components of PPG signal have been employed for other purposes, such as non-invasive haemodynamic monitoring. Perfusion index (PI) is derived from PPG signal and represents the ratio of pulsatile on non- pulsatile light absorbance or reflectance of the PPG signal. PI determinants are complex and interlinked, involving and reflecting the interaction between peripheral and central haemodynamic characteristics, such as vascular tone and stroke volume. Recently, several studies have shed light on the interesting performances of this variable, especially assessing regional or neuraxial block success, and haemodynamic monitoring in anaesthesia, perioperative and intensive care. Nevertheless, no review has yet been published concerning the interest of PI in these fields. In this narrative review will be exposed first the physiological and pathophysiological determinants of PI, and then the mean to measure this value as well as its potential limitations. In the second part, the existing data concerning usefulness of PI in different clinical settings such as operating theatres, intensive care units and emergency departments will be presented and discussed. Finally, the perspectives concerning the use of PI and mentioned aspects that should be explored regarding this tool will be underlined.
• 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
• 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.
• 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