Publications

2021

• Use of a micromechanical approach to understand the mechanical behavior of solid propellants
  
  • de Francqueville Foucault
  • Diani Julie
  • Gilormini Pierre
  • Vandenbroucke Aude
  Mechanics of Materials, Elsevier, 2021, 153, pp.1-9. The development of new generations of propellants with better energetic properties may be hampered by unsatisfactory mechanical behaviors in terms of strength and toughness. A micromechanical approach is adopted to provide a better understanding of the existing links between the constitutive phase behaviors and the local damage, and the macroscopic mechanical behavior of these materials. Three model materials have been made and tested in uniaxial tension. The stress-strain responses were recorded while monitoring their volume changes that quantify the macroscopic damage. A qualitative description of the local damage was obtained thanks to scanning electron microscopy images of samples under loading. The micromechanical approach consists in finite elements analyses on periodic microstructures of non-regular polyhedral particles embedded in a soft matrix. An original microstructure generation tool has been developed specifically in order to obtain highly filled isotropic microstructures. Debonding at the matrix/filler interface was taken into account with a cohesive-zone model (CZM). The impact of the CZM parameters is discussed, in an effort to make the link between the CZM parameters and how the local damage appears and develops, and between the cohesive behavior and the shape of the macroscopic stress-stretch responses of the heterogeneous materials. (10.1016/j.mechmat.2020.103656)
  DOI : 10.1016/j.mechmat.2020.103656
• Fracture Diodes: Directional asymmetry of fracture toughness
  
  • Brodnik N R
  • Brach Stella
  • Long C M
  • Ravichandran G
  • Bourdin B
  • Faber K T
  • Bhattacharya K
  Physical Review Letters, American Physical Society, 2021. Toughness describes the ability of a material to resist fracture or crack propagation. It is demonstrated here that fracture toughness of a material can be asymmetric, i.e., the resistance of a medium to a crack propagating from right to left can be significantly different from that to a crack propagating from left to right. Such asymmetry is unknown in natural materials, but we show that it can be built into artificial materials through the proper control of microstructure. This paves the way for control of crack paths and direction, where fracture-when unavoidable-can be guided through pre-designed paths to minimize loss of critical components.
• Rate and loading path dependent constitutive model for Ti-6Al-4V titanium alloy subject to bird strike
  
  • Ruiz de Sotto Miguel
  • Longère Patrice
  • Doquet Véronique
  • Papasidero Jessica
  , 2021.
• Fast Simulation Of Temprature And Grain Growth In Directed Energy Deposition Additive Manufacturing
  
  • Weisz-Patrault Daniel
  • Sakout Sofia
  • Ehrlacher Alain
  , 2021. In this paper, a fast simulation of grain growth during directed energy deposition is presented. Controlling the microstructure is indeed essential to obtain the desired macroscopic behavior. We present a fast macroscopic simulation of temperature accounting for grain growth. The proposed approach relies on the coupling of recent contributions presenting: (i) a simulation of temperature in DED, (ii) a mesoscopic model of grain growth model based on Orientated Tessellation Updating Method, and (iii) a macroscopic stochastic model of grain growth. The general strategy is to compute the temperature field as a function of time during the entire process. The initial crystallization is not addressed in this contribution, and an arbitrary initial microstructure are introduced to test the model. The stochastic evolution of the grain structure due to thermal cycling is computed, and the final grain structure statistics is obtained in the entire part. The proposed model is sufficiently fast to enable simulations of large parts and parametric studies or optimization loops can be performed to adjust process parameters. (10.23967/wccm-eccomas.2020.143)
  DOI : 10.23967/wccm-eccomas.2020.143
• Sequential data assimilation for mechanical systems with complex image data: application to tagged-MRI in cardiac mechanics
  
  • Imperiale Alexandre
  • Chapelle Dominique
  • Moireau Philippe
  Advanced Modeling and Simulation in Engineering Sciences, Springer, 2021, 8, pp.2 (47 p.). Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison-called discrepancy measure-is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction-correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that-via regional estimation of the above parameters-the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis. (10.1186/s40323-020-00179-w)
  DOI : 10.1186/s40323-020-00179-w
• Passive viscoelastic response of striated muscles
  
  • Staniscia Fabio
  • Truskinovsky Lev
  , 2021. Muscle cells with sarcomeric structure exhibit highly nontrivial passive mechanical response. The difficulty of its continuum modeling is due to the presence of long-range interactions transmitted by extended protein skeleton. To build a rheological model for muscle 'material' we use a stochastic micromodel and derive a linear response theory for a half-sarcomere. Instead of the first order rheological equation, anticipated by A.V. Hill on the phenomenological grounds, we obtain a novel second order equation. We use the values of the microscopic parameters for frog muscles to show that the proposed rheological model is in excellent quantitative agreement with physiological experiments.
• 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
• 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
• 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
• Quantifying the effect of two-point correlations on the effective elasticity of specific classes of random porous materials with and without connectivity
  
  • Zerhouni Othmane
  • Brisard Sébastien
  • Danas Kostas
  International Journal of Engineering Science, Elsevier, 2021, 166, pp.103520. It is well-known by now that the Hashin-Shtrikman bounds imply that the two-point correlation functions are not in general sufficient to estimate accurately the response of composites, especially when their underlying phases exhibit infinite contrast, e.g., porous materials. Starting from this longstanding, albeit qualitative result, this work investigates quantitatively the relevance of using two-point correlations to model the effective elastic properties of specific isotropic porous materials with and without connectivity. To achieve this in an unambiguous manner, we propose three different microstructures that share almost identical two-point statistics by design but are rather different morphologically. The choice of these microstructures is driven by their wide use in several practical problems ranging from polymers to geomaterials. The first microstructure is obtained by a random sequential adsorption (RSA) of non-overlapping, polydisperse, spherical and ellipsoidal voids oriented randomly in a unit-cell. The second one, termed connected random sequential adsorption (CRSA), is obtained from the first one by adding controlled connectivity via cylindrical channels of circular cross-section. The porosity resulting from connectivity is compensated by reducing the size of the existing voids to have the same overall porosity. Interestingly, we find that connectivity does not affect the corresponding two-point statistics. Finally, using as an input the numerical one-and two-point correlations of the RSA, we reconstruct a thresholded Gaussian random field (TGRF) microstructure. Using FFT numerical simulations, we show that the resulting effective elastic properties are very different for the three generated microstructures, despite them sharing nearly the same two-point correlation functions. We show, further, that the introduction of connectivity, and in particular the partial volume fraction of the connected channels, even small, affects strongly the resulting effective elasticity of the composite. (10.1016/j.ijengsci.2021.103520)
  DOI : 10.1016/j.ijengsci.2021.103520
• Stochastic nonlinear model for somatic cell population dynamics during ovarian follicle activation
  
  • Clément Frédérique
  • Robin Frédérique
  • Yvinec Romain
  Journal of Mathematical Biology, Springer, 2021, 82 (3), pp.1-52. In mammals, female germ cells are sheltered within somatic structures called ovarian follicles, which remain in a quiescent state until they get activated, all along reproductive life. We investigate the sequence of somatic cell events occurring just after follicle activation, starting by the awakening of precursor somatic cells, and their transformation into proliferative cells. We introduce a nonlinear stochastic model accounting for the joint dynamics of the two cell types, and allowing us to investigate the potential impact of a feedback from proliferative cells onto precursor cells. To tackle the key issue of whether cell proliferation is concomitant or posterior to cell awakening, we assess both the time needed for all precursor cells to {awake}, and the corresponding increase in the total cell number with respect to the initial cell number. Using the probabilistic theory of first passage times, we design a numerical scheme based on a rigorous Finite State Projection and coupling techniques to compute the mean extinction time and the cell number at extinction time. We find that the feedback term clearly lowers the number of proliferative cells at the extinction time. We calibrate the model parameters using an exact likelihood approach. We carry out a comprehensive comparison between the initial model and a series of submodels, which helps to select the critical cell events taking place during activation, and suggests that awakening is prominent over proliferation. (10.1007/s00285-021-01561-x)
  DOI : 10.1007/s00285-021-01561-x
• Left ventricular torsion obtained using equilibrated warping in patients with repaired Tetralogy of Fallot
  
  • Castellanos Daniel Alexander
  • Škardová Kateřina
  • Bhattaru Abhijit
  • Berberoglu Ezgi
  • Greil Gerald
  • Tandon Animesh
  • Dillenbeck Jeanne
  • Burkhardt Barbara
  • Hussain Tarique
  • Genet Martin
  • Chabiniok Radomir
  Pediatric Cardiology, Springer Verlag, 2021, 42 (6), pp.1275-1283. Purpose: Patients after surgical repair of Tetralogy of Fallot (rTOF) may suffer a decrease in left ventricular (LV) function. The aim of our study is to evaluate a novel method of assessing LV torsion in patients with rTOF, as an early indicator of systolic LV dysfunction. Methods: Motion tracking based on image registration regularized by the equilibrium gap principle, known as equilibrated warping, was employed to assess LV torsion. Seventy-six cases of rTOF and ten normal controls were included. The group of controls was assessed for reproducibility using both equilibrated warping and standard clinical tissue tracking software (CVI42, version 5.10.1, Calgary, Canada). Patients were dichotomized into two groups: normal vs. loss of torsion. Results: Torsion by equilibrated warping was successfully obtained in 68 of 76 (89%) patients and 9 of 10 (90%) controls. For equilibrated warping, the intra- and inter-observer coefficients of variation were 0.095 and 0.117, respectively; compared to 0.260 and 0.831 for tissue tracking by standard clinical software. The intra- and inter-observer intraclass correlation coefficients for equilibrated warping were 0.862 and 0.831, respectively; compared to 0.992 and 0.648 for tissue tracking. Loss of torsion was noted in 32 of the 68 (47%) patients with rTOF. There was no difference in LV or RV volumes or ejection fraction between these groups. Conclusion: The assessment of LV torsion by equilibrated warping is feasible and shows good reliability. Loss of torsion is common in patients with rTOF and its robust assessment might contribute into uncovering heart failure in an earlier stage. (10.1007/s00246-021-02608-y)
  DOI : 10.1007/s00246-021-02608-y
• Pressure-driven micro-poro-mechanics: A variational framework for modeling the response of porous materials
  
  • Álvarez-Barrientos Felipe
  • Hurtado Daniel E
  • Genet Martin
  International Journal of Engineering Science, Elsevier, 2021, 169, pp.103586. Porous materials are highly relevant in engineering and medical applications due to their enhanced properties and lightweight nature. Current micromechanical models of porous materials can accurately predict the response under the assumptions of small deformations and drained conditions, typically driven by imposed deformations. However, the theoretical framework for the micromechanical modeling of porous material driven by pore pressure in the large-deformation range has been understudied. In this work, we develop a finite-deformation variational framework for pressure-driven foams, i.e., materials where the pore pressure in the cavities produces the deformation. We further consider different kinematical constraints in the formulation of boundary conditions: kinematic uniform displacements, periodic displacements and uniform traction. We apply the proposed model in the numerical simulation of lung porous tissue using a spherical alveolar geometry and an image-based geometry obtained from micro-computed-tomography images of rat lung. Our results show that the stress distributions in the spherical alveolar model are highly dependent on the kinematical constraints. In contrast, the stress distribution in the image-based alveolar model is not affected by the choice of boundary conditions. Further, when comparing the response of pressure-driven versus deformation-driven models, we conclude that hydrostatic stresses experience a marked shift in their distribution, whereas the deviatoric stresses remain unaffected. Our findings of how stresses are affected by the choice of boundary conditions and geometry take particular relevance in the simulation of the lungs, where the pressure-driven and deformation-driven cases are related to mechanical ventilation and spontaneous breathing. (10.1016/j.ijengsci.2021.103586)
  DOI : 10.1016/j.ijengsci.2021.103586
• Personalized Pulmonary Poromechanics in Health and Idiopathic Pulmonary Fibrosis
  
  • Genet Martin
  • Patte Cécile
  • Fetita Catalin
  • Brillet Pierre-Yves
  • Chapelle Dominique
  , 2021.
• Brain fragility among middle-aged and elderly patients from electroencephalogram during induction of anaesthesia
  
  • Cartailler Jerome
  • Touchard Cyril
  • Parutto Pierre
  • Gayat Etienne
  • Paquet Claire
  • Vallée Fabrice
  European Journal of Anaesthesiology, Lippincott, Williams & Wilkins, 2021, 38 (12), pp.1304-1306. Cognitive decline (CD) is a common condition amongst elderly, affecting memory, language or thinking. Patients experiencing CD have a higher incidence rate of post-operative neurocognitive disorders 1. Moreover, for a fraction of these patients, (10.1097/EJA.0000000000001524)
  DOI : 10.1097/EJA.0000000000001524
• Bifurcation of magnetorheological film–substrate elastomers subjected to biaxial pre-compression and transverse magnetic fields
  
  • Rambausek M.
  • Danas Kostas
  International Journal of Non-Linear Mechanics, Elsevier, 2021, 128, pp.103608. This work investigates the primary sinusoidal bifurcation wrinkling response of single-and multi-layered magne-torheological elastomer (MRE) film-substrate systems subjected to combined transverse applied magnetic fields and in-plane biaxial pre-compression. A recently proposed continuum model that includes the volume fraction of soft-magnetic particles is employed to analyze the effect of the magnetic properties upon the bifurcation response of the system. The analysis is built in a highly versatile manner using a finite-element discretization approach along the direction of the applied magnetic field and Fourier expansions along the infinite in-plane layer directions. This allows for a seamless investigation of various multi-layered structures. First, we analyze the effect of biaxial pre-compression upon the critical magnetic field for a film-substrate system and for various mechanical stiffness ratios. We observe a kink in the critical magnetic curves and a reflection in the corresponding wave numbers as they cross the equi-biaxial pre-compression regime. Subsequently, we consider a MRE film bonded to a MRE substrate and study the effect of the particle volume fraction ratios in those two parts. As a result, we obtain sharp pattern transitions, i.e., long to short wavelengths changes with only minor perturbations of the applied pre-compression. The presence of a magnetic sub-strate changes qualitatively and quantitatively the bifurcation response of the film/substrate system. Finally, we carry out a data-mining exercise to minimize the critical magnetic field at bifurcation by using three different topologies, i.e., a monolayer, a bilayer and a sandwich film. We find that the topologies resembling closely the monolayer one lead to the lowest critical magnetic fields for a given biaxial pre-compression. (10.1016/j.ijnonlinmec.2020.103608)
  DOI : 10.1016/j.ijnonlinmec.2020.103608
• Criterion for critical junctions in elastic-plastic adhesive wear
  
  • Brach Stella
  • Collet Sylvain
  Physical Review Letters, American Physical Society, 2021. We investigate elastic-plastic adhesive wear via a continuum variational phase-field approach. The model seamlessly captures the transition from perfectly brittle, over quasi-brittle to elastic-plastic wear regimes, as the ductility of the contacting material increases. Simulation results highlight the existence of a critical condition that morphological features and material ductility need to satisfy for the adhesive junction to detach a wear debris. We propose a new criterion to discriminate between non-critical and critical asperity contacts, where the former produce negligible wear while the latter lead to significant debris formation.
• A penalty-free approach to PDE constrained optimization: Application to an inverse wave problem
  
  • Hoffmann Alexandre
  • Monteiller Vadim
  • Bellis Cédric
  Inverse Problems, IOP Publishing, 2021, 37 (5).
• Quantification of Left Ventricular Strain by Joint Analysis of 3D Tagging and Cine MR Images
  
  • Berberoglu Ezgi
  • Stoeck Christian
  • Kozerke Sebastian
  • Genet Martin
  , 2021.
• Effects of particles size on the overall strength of nanocomposites: Molecular Dynamics simulations and theoretical modeling
  
  • Lucchetta Antoine
  • Brach Stella
  • Kondo Djimédo
  Mechanics Research Communications, Elsevier, 2021. We perform Molecular Dynamics simulations to investigate the strength properties of particulate reinforced nanocomposites. For a fixed reinforcement volume fraction, the effective strength increases as the inclusion size decreases. We further develop a kinematic limit analysis approach, which delivers theoretical estimates of the effective strength. The model is first assessed in the absence of size effects by comparison with data from available literature. An extension to nanocomposites is then proposed, accounting for the presence of surface stresses at the matrix/inclusion interface. Numerical data are used to calibrate the interfacial strength, which is found to be a size-dependent property.
• Crushing of additively manufactured thin-walled metallic lattices: Two-scale strain localization analysis
  
  • Balit Yanis
  • Margerit Pierre
  • Charkaluk Eric
  • Constantinescu Andrei
  Mechanics of Materials, Elsevier, 2021, 160, pp.103915. The response of architectured structures is characterized by multi-scale kinematics, which complex relation and effect on the engineering load response is still not completely understood and therefore needs further investigations. More precisely, the lack of experimental methods enabling to provide multi-scale data remains a key issue. The paper presents an experimental and numerical analysis of crushing tests performed on thin-walled auxetic metallic lattices manufactured by Directed Energy Deposition. The work is focused on the two-scale strain localization occurring (a) at the microscopic scale of the unit cell and (b) at the macroscopic scale corresponding to the homogenized continuum. The structures of interest are defined as the extrusion of a 2D auxetic wireframe and allow the application of an adapted digital image correlation scheme dedicated to the identification of the kinematics at the two considered scales. In particular, the microscopic kinematics are studied by following the deformation of lattice crossings, while the macroscopic strains are deduced from the motion of virtual unit cell corners. The results show that the global elastic-plastic response of the lattices is completely driven by the formation of plastic hinges at specific locations, leading to characteristic deformation patterns and eventually a collective behavior of neighboring unit cells. Companion finite element computations show an excellent match with experiments and thus enable to assess the effect of modeling assumptions, unit cell geometry, strain rate and geometrical imperfections in the global response of the architecture material. (10.1016/j.mechmat.2021.103915)
  DOI : 10.1016/j.mechmat.2021.103915
• Signed-distance function based non-rigid registration of image series with varying image intensity
  
  • Škardová Kateřina
  • Oberhuber Tomáš
  • Tintěra Jaroslav
  • Chabiniok Radomir
  Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2021, 14 (3), pp.1145-1160. In this paper we propose a method for locally adjusted optical flow-based registration of multimodal images, which uses the segmentation of the object of interest and its representation by the signed-distance function (OF dist method). We deal with non-rigid registration of the image series acquired by the Modiffied Look-Locker Inversion Recovery (MOLLI) magnetic resonance imaging sequence, which is used for a pixel-wise estimation of T 1 relaxation time. The spatial registration of the images within the series is necessary to compensate the patient's imperfect breath-holding. The evolution of intensities and a large variation of image contrast within the MOLLI image series, together with the myocardium of left ventricle (the object of interest) typically not being the most distinct object in the scene, makes the registration challenging. The paper describes all components of the proposed OF dist method and their implementation. The method is then compared to the performance of a standard mutual information maximization-based registration method, applied either to the original image (MIM) or to the signed-distance function (MIM dist). Several experiments with synthetic and real MOLLI images are carried out. On synthetic image with a single object, MIM performed the best, while OF dist and MIM dist provided better results on synthetic images with more than one object and on real images. When applied to signed-distance function of two objects of interest, MIM dist provided a larger registration error (but more homogeneously distributed) compared to OF dist. For the real MOLLI image series with left ventricle pre-segmented using a level-set method, the proposed OF dist registration performed the best, as is demonstrated visually and by measuring the increase of mutual information in the object of interest and its neighborhood. (10.3934/xx.xx.xx.xx)
  DOI : 10.3934/xx.xx.xx.xx
• HARP-I: A Harmonic Phase Interpolation Method for the Estimation of Motion from Tagged MR Images
  
  • Mella Hernán
  • Mura Joaquín
  • Wang Hui
  • Taylor Michael D
  • Chabiniok Radomir
  • Tintera Jaroslav
  • Sotelo Julio
  • Uribe Sergio
  IEEE Transactions on Medical Imaging, Institute of Electrical and Electronics Engineers, 2021, 40 (4), pp.1240-1252. We proposed a novel method called HARP-I, which enhances the estimation of motion from tagged Magnetic Resonance Imaging (MRI). The harmonic phase of the images is unwrapped and treated as noisy measurements of reference coordinates on a deformed domain, obtaining motion with high accuracy using Radial Basis Functions interpolations. Results were compared against Shortest Path HARP Refinement (SP-HR) and Sine-wave Modeling (SinMod), two harmonic image-based techniques for motion estimation from tagged images. HARP-I showed a favorable similarity with both methods under noise-free conditions, whereas a more robust performance was found in the presence of noise. Cardiac strain was better estimated using HARP-I at almost any motion level, giving strain maps with less artifacts. Additionally, HARP-I showed better temporal consistency as a new method was developed to fix phase jumps between frames. In conclusion, HARP-I showed to be a robust method for the estimation of motion and strain under ideal and non-ideal conditions.
• 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