Publications

2026

• Homogenizing elastic lattices with mechanisms
  
  • Audoly Basile
  • Lestringant Claire
  • Nassar Hussein
  European Journal of Mechanics - A/Solids, Elsevier, 2026, 117, pp.105956. We propose an asymptotic method for homogenizing periodic elastic lattices that works in the presence of mechanisms, both of the macroscopic type (strain-producing modes) and of the microscopic type (internal modes). When a microscopic mechanism is present, the unit-cell problem produced by classical homogenization is singular. It can be fixed by including the amplitude~$\theta (\mathbf{X})$ of the mechanism as an additional macroscopic degree of freedom (enrichment variable) contributing to the effective energy via its gradient $\nabla \theta (\mathbf{X})$. When a macroscopic mechanism is present, homogenization delivers a degenerate effective energy at leading order, which can be regularized by accounting for the strain gradient. We introduce an asymptotic second-order homogenization scheme that integrates these two features: it delivers an effective energy capturing both the strain-gradient effect $\nabla \mathbf{\varepsilon} (\mathbf{X})$ relevant to macroscopic mechanisms, and the $\nabla \theta (\mathbf{X})$ regularization relevant to microscopic mechanisms, if any is present. The versatility of the approach is illustrated with a selection of lattices displaying a variety of effective behaviors. It follows a unified pattern that leads to a classification of these effective behaviors. Whereas the procedure delivers known effective models for elastic lattices without mechanisms, it can generate novel effective models for lattices possessing mechanisms. (10.1016/j.euromechsol.2025.105956)
  DOI : 10.1016/j.euromechsol.2025.105956
• Stability of time stepping methods for discontinuous Galerkin discretizations of Friedrichs' systems
  
  • Imperiale Sébastien
  • Joly Patrick
  • Rodríguez Jerónimo
  , 2025. In this work we study new various energy-based theoretical results on the stability of s-stages, s-th order explicit Runge-Kutta integrators as well as a modified leap-frog scheme applied to discontinuous Galerkin discretizations of transient linear symmetric hyperbolic Friedrichs' systems. We restrict the present study to conservative systems and Cauchy problems.
• A class of optimal virtual fields for inverse problems in elasticity
  
  • Chibli Nagham
  • Genet Martin
  • Imperiale Sébastien
  , 2026. This work addresses the identification of nonhomogeneous constitutive parameters from full-field measurements in both linear and nonlinear elasticity, considering incompressible as well as compressible materials. The inverse identification procedure relies on the Virtual Fields Method (VFM), which is based on the principle of virtual work with specifically chosen virtual fields. We propose an optimal class of virtual fields, designed to optimize the reconstruction stability with respect to measurement noise. A series of numerical experiments illustrate the effectiveness of the proposed approach. The method exhibits moderate sensitivity to measurement noise and remains robust even when the boundary conditions are only partially known.
• Continuous microstructure variations with graded properties in directed energy deposition
  
  • Bréhier Michèle
  • Weisz-Patrault Daniel
  • Tournier Christophe
  Additive Manufacturing Letters, Elsevier, 2026, 17, pp.100372. <div><p>Directed energy deposition additive manufacturing is a versatile technique for fabricating complex geometries, where precise control of process parameters is crucial for tailoring microstructure and part properties. Microstructure control strategies usually involve variation of material composition (i.e., functionally graded materials) or interlayer time delay. However, the obtained microstructures are usually uniform in the print direction and exhibit sharp transitions from one layer to the next in the build direction. This paper targets continuous microstructural variation by exploiting active cooling strategies to control cooling conditions. To do so, the scanning speed is continuously varied, necessitating accommodating the bead size variations with non-standard trajectory generation based on a phenomenological law. The proposed strategy is demonstrated on thin-wall structures made of IN718 using a powder-based laser directed energy deposition. The results reveal a continuous microstructural transition along the print direction, characterized by two distinct microstructural regimes with markedly different morphological features and crystallographic textures. This demonstrates the capability of scanning speed modulation to engineer heterogeneous microstructures within a single component, offering insights into tailoring material properties for specific engineering applications.</p></div> (10.1016/j.addlet.2026.100372)
  DOI : 10.1016/j.addlet.2026.100372
• A new surrogate microstructure generator for porous materials with applications to the buffer layer of TRISO nuclear fuel particles
  
  • Eisenhardt Philipp
  • Khristenko Ustim
  • Wohlmuth Barbara
  • Constantinescu Andrei
  Journal of Nuclear Materials, Elsevier, 2026, 624, pp.156498. (10.1016/j.jnucmat.2026.156498)
  DOI : 10.1016/j.jnucmat.2026.156498
• Locally implicit and stabilized explicit time schemes for transient visco-elastic wave propagation problems
  
  • Vasanthan Vinduja
  • Imperiale Alexandre
  • Imperiale Sébastien
  Journal of Numerical Mathematics, De Gruyter, 2026. In the context of numerical methods for time-domain wave propagation problems, combining high-order lumped finite elements with an explicit time scheme is a popular approach for either inviscid or visco-elastic models. This strategy has proven to be efficient in numerous cases. However, when dealing with non-uniform meshes or high-contrast materials, the stability condition on the time step becomes drastically stringent. One can encounter such configurations when meshing unfortunate CAD input le, e.g. when dealing with heterogeneous materials where neighboring heterogeneities produce very small elements in-between them, or when considering materials with high and localized wave velocities. To address efficiently these configurations, we propose to adapt the locally implicit and stabilized leapfrog methods to the Kelvin-Voigt, Maxwell and Zener visco-elastic models. We prove using energy arguments that the global stability condition of these schemes can be much more favorable compared to a fully-explicit scheme, decreasing the number of iterations for a fixed time window. We illustrate our approaches with 2D and 3D numerical test cases related to ultrasonic non-destructive testing experiments. (10.1515/jnma-2025-0044)
  DOI : 10.1515/jnma-2025-0044
• Stamps for Pattern Applications for DIC or Markers Tracking
  
  • Diani J.
  • Geraud G.
  • Coq A.
  • Kuzyara V.
  Experimental Techniques, Society for Experimental Mechanics, 2026. Digital image correlation requires a surface pattern to monitor deformation, and while spray paint is widely used for this purpose, it suffers from drawbacks such as limited reproducibility and poor control over speckle characteristics. This study aims to develop stamps to apply patterns with greater consistency and control, and to demonstrate that such pattern speckle performs comparably to traditional spray paint speckle. For that purpose, speckles were applied to polymer surfaces using two techniques, ink stamping of circular dots and conventional spray painting. Their quality was first evaluated through numerical assessments, followed by digital image correlation analyses under both small and large strains. Small-strain behavior was studied using synthetically deformed images based on sinusoidal displacements, while large-strain performance was assessed via uniaxial stretching of a holed elastomer sample. Both speckle application methods yielded similar results in terms of image correlation accuracy and robustness across deformation scales proving that the produced stamps offer a viable alternative to spray paint, providing significant advantages in terms of control, reproducibility, and customizability of the speckle pattern, without compromising performance. (10.1007/s40799-026-00875-z)
  DOI : 10.1007/s40799-026-00875-z
• Rapid estimation of microstructure using infrared imaging and solidification modeling in wire-laser directed energy deposition
  
  • Dollé Quentin
  • Bréhier Michèle
  • Berté Emmanuel
  • Witz Jean-Francois
  • Tournier Christophe
  • El Bartali Ahmed
  • Weisz-Patrault Daniel
  , 2026. The widespread deployment of Directed Energy Deposition Additive Manufacturing is limited by the lack of control over the produced material depending on process parameters: in particular, the microstructure resulting from rapid solidification. While cost-efficient numerical simulations have been developed to predict temperature evolution and microstructure, their reliability hinges on high-quality experimental validation. This study first addresses this challenge by introducing a simple and cost-effective infrared measurement procedure that combines a single-band camera and a dual-band pyrometer to quantitatively measure temperature fields during wire-laser DED. To do so, the apparent emissivity field was identified and found to be highly heterogeneous due to localized cover gas and oxidation. In addition, to enable rapid microstructure estimation, fast computational procedures are proposed to (i) calculate the thermal gradient field using Fast Fourier Transform, and (ii) simulate solidification in the melt pool, including competitive growth between columnar dendritic grains, using a recent Voronoi tessellation-based model. The computation time is compatible with the development of an online monitoring procedure. The resulting microstructure predictions were validated against Electron Backscatter Diffraction measurements, demonstrating excellent qualitative agreement. This work validates the proposed approach as a promising tool for closed-loop control of microstructure during DED.
• One- and Two-Photon Polymerization of Solvent- and Filler-Free Aromatic Organic Precursors: Toward 3D-Printed Semiconducting Microstructures
  
  • Noè Camilla
  • Laroui Sami
  • Zucchi Gaël
  • Bodelot Laurence
  ACS Applied Engineering Materials, ACS, 2026, 4 (2), pp.926-935. Over the past decades, a great deal of attention has been dedicated toward developing semiconductive polymers (SP), which are now considered as a critical class of photoactive and electroactive materials. However, the processing of many SPs involves the use of solvents, leading to the fabrication of samples with limited shapes, mostly flat 2D thin films. To develop 3D-shaped materials with potential semiconducting properties, this work tackles the development of solvent-and filler-free resins for the fabrication via additive manufacturing of microscale organic semiconductors. Two molecular liquids based on electron-rich carbazole and triarylamine units are used to formulate photoresists. The successful reactivity of the formulations was investigated, both at the macroscopic scale (one-photon polymerization through UV curing) and at the microscopic scale (two-photon polymerization (2PP) via direct laser writing), with Fourier transform infrared spectroscopy (FT-IR) and Raman spectroscopy. Subsequently, the thermal properties of the macroscopic samples were investigated by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Optimization of the printing parameters for 2PP led to the elaboration of 3D micrometer-scale samples whose morphology was assessed by scanning electron microscopy (SEM). Finally, electrical measurements revealed a semiconducting behavior as the samples were found to conduct current after p-doping with iodine. (10.1021/acsaenm.5c01101)
  DOI : 10.1021/acsaenm.5c01101
• A projection scheme for an incompressible soft material poromechanics model
  
  • Barré Mathieu
  • Grandmont Céline
  • Moireau Philippe
  , 2026. In this work, we propose and analyse a new scheme to discretize the linearized version of a rather general poromechanics model adapted to biological tissues perfusion. This model, which is related to – albeit different from – Biot equations, involves unsteady solid and fluid momentum balance equations that are further coupled through an incompressibility constraint, a pore pressure and permeability terms. The key feature of the scheme is to decouple the solid, fluid and pressure unknowns at each time step by means of a projection method, composed of a prediction and a correction step. We perform a complete stability analysis of the scheme depending on the implicit or explicit treatment of friction and pressure in the prediction step. Several boundary conditions are considered, including conditions coupling the solid and fluid phases on the boundary that are imposed at the discrete level using a Robin-Robin method. In the case of Dirichlet boundary conditions, we also provide a fully discrete error estimate as long as a discrete inf-sup condition is satisfied. The scheme properties and robustness with respect to physical parameters are illustrated by numerical experiments. Finally, its computational performance is compared with that of a monolithic approach.
• Mean stress effects and energy-based modeling of fatigue behavior in artificially cemented rock-like materials under cyclic loading
  
  • Darsanj Solmaz
  • Emami Tabrizi Mehrdad
  • Constantinescu Andrei
  Bulletin of Engineering Geology and the Environment, Springer Verlag, 2026, 85 (2), pp.113. (10.1007/s10064-025-04757-3)
  DOI : 10.1007/s10064-025-04757-3
• Asymptotic strain-gradient theory for one-dimensional continua
  
  • Thbaut Manon
  • Audoly Basile
  • Lestringant Claire
  Journal of the Mechanics and Physics of Solids, Elsevier, 2026, 206, pp.106392. (10.1016/j.jmps.2025.106392)
  DOI : 10.1016/j.jmps.2025.106392
• Finite element modelling for the reproduction of dynamic OCE measurements in the cornea
  
  • Merlini Giulia
  • Imperiale Sébastien
  • Allain Jean-Marc
  Journal of the Mechanics and Physics of Solids, Elsevier, 2026, 206, pp.106363. Recent advances in dynamic elastography, particularly through optical coherence tomography combined with transient excitations have enabled rapid, localized, and non-invasive mechanical data acquisition of the cornea. This dataopens the path to early-detection of pathologies and more accurate treatment. However, the analysis of the wave propagation is a complex mechanical problem: the cornea is a structure under pressure, with non-linear material behavior. Thus, computational analysis are needed to extract mechanical parameters from the data. In this study, we present a time-dependent finite element model for the reproduction of transient shear wave elastographic measurements in the cornea. The mechanical problem consists in a smallamplitude wave propagating in the cornea, largely deformed by intraocular pressure in physiological conditions. The model accounts for anisotropic, hyperelastic, and incompressible behavior of the cornea, as well as its accurate geometry, and the preloaded condition. We have implemented two different numerical approaches to solve first the static non-linear inflation of the cornea and then the linear wave propagation problem to reproduce the measurements. We investigate the impact of material anisotropy and prestress on wave propagation and demonstrate that intraocular pressure critically influences shear wave velocity. Additionally, by introducing a localized mechanical defect to simulate a pathological defect, we show that simulated shear wave can detect and quantify mechanical weaknesses, suggesting potential as a diagnostic tool to assess corneal health. (10.1016/j.jmps.2025.106363)
  DOI : 10.1016/j.jmps.2025.106363
• SCAR : a self-consistent recurrent cell for real-time finite strain elastoplastic simulations
  
  • Lesueur Louis
  • Weisz-Patrault Daniel
  • Thorin Anders
  , 2026. Complex fabrication and forming processes operating under finite strains could benefit significantly from optimization loops of process parameters, which are often hindered by the prohibitive computational costs of process modeling. Neural networks present a promising solution to derive fast and accurate surrogate models, thereby enabling such optimizations. Furthermore, many processes involve substantial inherent variability, and hence often require manual process control. Neural networks could also provide real-time predictions that would greatly assist in decision-making. Although recursive neural networks have been applied in mechanics, their use in modeling elastoplastic behavior at finite strains remains underexplored. This paper introduces a new family of self-consistent recurrent cells, referred to as SCAR. These cells are specifically designed to address history-dependent problems, such as elastoplasticity, and ensure compliance with key properties required for such applications. To evaluate the SCAR cells, a generic architecture named PlastiNN, featuring a spatially resolved neural decoder, is employed. This approach results in faster training times and more accurate predictions in comparison to commonly used architectures. Additionally, PlastiNN can accommodate a series of successive loads on a workpiece, which is critical for most fabrication and forming processes. The effectiveness of this strategy is demonstrated by comparing SCAR cells to other recurrent cells within the PlastiNN architecture through a comprehensive benchmark including two datasets of 1D and 3D simulations, ranging from challenging toy applications to more realistic industrial test cases. Results highlight the superiority of the proposed recurrent neural network architecture for modeling elastic-plastic behavior at finite strains in engineering processes.
• A stationarity principle generating effective boundary conditions for second-order homogenization
  
  • Thbaut Manon
  • Audoly Basile
  • Lestringant Claire
  Journal of Elasticity, Springer Verlag, 2026, 158 (1), pp.15. We derive an effective model for a periodic chain of linearly-elastic springs, achieving second-order accuracy in the scale separation parameter $\varepsilon \ll 1$. The chain has finite length and is made up of springs connecting both nearest- and next-nearest-neighbors: it serves as a one-dimensional prototype for higher-order periodic homogenization problems with boundaries. This type of problem has been approached by inserting two-scale expansions into the equations of equilibrium in the bulk and by matching them with boundary-layer solutions. We explore an alternative method operating at the energy level, bypassing the cumbersome matching procedure. We start from an ansatz of the microscopic displacement accounting for both boundary layers and for small-scale fluctuations in the bulk, and insert it into the discrete energy. This yields a continuous energy functional depending on the macroscopic displacement $u$, in the form of a series expansion in powers of $\varepsilon$. We call it a {\tmem{pseudo-energy}} $\Phi_{\varepsilon} [u]$ as it is not positive when truncated at order~$\varepsilon^2$. The boundary terms in the pseudo-energy account for boundary layers in an effective way. By making the pseudo-energy stationary order by order in $\varepsilon$, we derive the homogenized equations of equilibrium along with effective boundary conditions. We provide quantitative validation showing that the effective model is correct to second order. We point out the special form of the effective higher-order tractions, which has been overlooked in strain-gradient theories proposed so far. (10.1007/s10659-026-10190-8)
  DOI : 10.1007/s10659-026-10190-8
• Community challenge towards consensus on characterization of biological tissue: C4Bio’s first findings
  
  • Famaey Nele
  • Fehervary Heleen
  • Lafon Yoann
  • Akyildiz Ali
  • Dreesen Silke
  • Bruyère-Garnier Karine
  • Allain Jean-Marc
  • Alloisio Marta
  • Aparici-Gil Alejandro
  • Catalano Chiara
  • Chassagne Fanette
  • Chokhandre Snehal
  • Crevits Kimberly
  • Crielaard Hanneke
  • Cunnane Eoghan
  • Cunnane Connor
  • de Leener Karen
  • Desai Amisha
  • Driessen Rob
  • Erdemir Ahmet
  • Eskandari Mona
  • Evans Sam
  • Gasser Christian
  • Gebhardt Marc
  • Glasmacher Birgit
  • Holzapfel Gerhard
  • Isasi Mikel
  • Jennings Louise
  • Kurz Sascha
  • Leal-Marin Sara
  • Lecomte Pauline
  • Morch Annie
  • Mulvihill John
  • Nemavhola Fulufhelo
  • Pandelani Thanyani
  • Pasta Salvatore
  • Peña Estefania
  • Pierrat Baptiste
  • Ploeg Heidi-Lynn
  • Polzer Stanislav
  • Rausch Manuel
  • Schwarz David
  • Screen Hazel
  • Sherifova Selda
  • Sommer Gerhard
  • Wang Shengzhang
  • Walsh Darragh
  • Yadav Deepesh
  • Marchal Thierry
  • Geris Liesbet
  Journal of Biomechanics, Elsevier, 2026, 194, pp.113021. This study investigates methodological variability across various expert laboratories worldwide, with regards to characterizing the mechanical properties of biological tissues. Two testing rounds were conducted on the specific use case of uniaxial tensile testing of porcine aorta. In the first round, 24 labs were invited to apply their established methods to assess inter-laboratory variability. This revealed significant methodological diversity and associated variability in the stress–stretch results, underscoring the necessity for a standardized approach. In the second round, a consensus protocol was collaboratively developed and adopted by 19 labs in an attempt to minimize variability. This involved standardized sample preparation and uniformity in testing protocol, including the use of a common cutting and thickness measurement tool. Despite protocol harmonization, significant variability persisted across labs, which could not be solely attributed to inherent biological differences in tissue samples. These results illustrate the challenges in unifying testing methods across different research settings, underlining the necessity for further refinement of testing practices. Enhancing consistency in biomechanical experiments is pivotal when comparing results across studies, as well as when using the resulting material properties for in silico simulations in medical research. (10.1016/j.jbiomech.2025.113021)
  DOI : 10.1016/j.jbiomech.2025.113021
• Micro-Poro-Mechanical Modeling of The Lung Parenchyma: Theoretical Modeling and Parameters Identification
  
  • Manoochehrtayebi Mahdi
  • Genet Martin
  • Bel-Brunon Aline
  Journal of Biomechanical Engineering, American Society of Mechanical Engineers, 2026, 148 (1), pp.BIO-25-1063. Micro-poro-mechanical approaches can be employed to simulate the behavior of porous media, such as lung parenchyma, with respect to their microscopic morphological and mechanical features. In this work, we propose a general micromechanical framework to describe the behavior of a porous hyperelastic material in large strains, including surface tension, and adapt its parameters to reproduce lung parenchyma behavior. We illustrate the method on a 2D periodic microstructure. The modeling framework is adaptable to any microstructure and any combination of stress, strain and pressure loadings.The identification of the model parameters in the context of lung parenchyma, based on existing experimental morphological and pressure-volume data, is performed sequentially. 12 parameters related to morphology, alveolar wall constitutive behavior and surface tension are calibrated to reproduce pressure-volume curves in various conditions, for a porosity in the unloaded state set to Φf0 =63%. The calibrated alveolar diameter is Dalv = 54 μm. The identifiability of the Neohookean and Ogden-Ciarlet-Geymonat hyperelastic potential parameters is studied; their values are β1 = 94.3 Pa, β2 = 16.9 Pa, β3 = 619 Pa and α = 3.154. The hysteretic response of lung to pressure is reproduced thanks to the formulation of a surface-dependent surface tension. This work paves the way for a better understanding of the relationship between microscopic features and the macroscopic response of lung, in healthy and pathological conditions. Further experimental investigations could help confirming the ranges of parameters obtained in this study. (10.1115/1.4070036)
  DOI : 10.1115/1.4070036
• Stability analysis of a new curl-based full field reconstruction method in 2D isotropic nearly-incompressible elasticity
  
  • Chibli Nagham
  • Genet Martin
  • Imperiale Sébastien
  Inverse Problems, IOP Publishing, 2026. In time-harmonic elastography, the shear modulus is typically inferred from full field displacement data by solving an inverse problem based on the time-harmonic elastodynamic equation. In this paper, we focus on nearly incompressible media, which pose robustness challenges, especially in the presence of noisy data. Restricting ourselves to 2D and considering an isotropic, linearly deforming medium, we reformulate the problem as a non-autonomous hyperbolic system and, through theoretical analysis, establish existence, uniqueness, and stability of the inverse problem. To ensure robustness with noisy data, we propose a least-squares approach with regularization. The convergence properties of the method are verified numerically using in silico data.