Publications

2026

• 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
• 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
• Assessment of Human Corneal Biomechanical Properties After Refractive Surgery With Inflation Test Using Optical Coherence Tomography
  
  • Memmi Benjamin
  • Wu Qian
  • Borderie Vincent
  • Allain Jean-Marc
  Journal of Refractive Surgery, Slack, 2026, 42 (1), pp.64-70. The incidence of myopia is currently increasing worldwide. It is becoming a significant public health issue, with billions of people (ie, 49.8% of the world population) estimated to be affected by this condition by 2050. Refractive surgery is a corneal surgery that treats myopia by modifying the shape of the cornea. Photorefractive keratectomy (PRK), laser in situ keratomileusis (LASIK), and small incision lenticule extraction (SMILE) are three mainstay refractive surgeries worldwide. Recent advances, specifically in the understanding of the biomechanical properties of the cornea and its response to diseases and surgical interventions, have significantly improved the safety and surgical outcomes of corneal refractive surgery, whose popularity and demand continue to grow worldwide. However, iatrogenic keratectasia resulting from the deterioration in corneal biomechanics caused by surgical interventions, although rare, remains a global concern. In vivo biomechanical evaluation, enabled by clinical imaging systems such as the ORA (Reichert Technologies) and the Corvis ST (Oculus Optikgeräte GmbH), has significantly improved the risk profiling of patients for iatrogenic keratectasia. (10.3928/1081597x-20251202-03)
  DOI : 10.3928/1081597x-20251202-03
• 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.
• 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.
• 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. We present a surrogate material model for generating microstructure samples reproducing the morphology of the real material. The generator is based on Gaussian random fields, with a Matérn kernel and a topological support field defined through ellipsoidal inclusions clustered by a random walk algorithm. We identify the surrogate model parameters by minimizing misfits in a list of statistical and geometrical descriptors of the material microstructure. To demonstrate the effectiveness of the method for porous nuclear materials, we apply the generator to the buffer layer of Tristructural Isotropic Nuclear Fuel (TRISO) particles. This part has been shown to be a failure sensitive part of TRISO nuclear fuel and our generator is optimized with respect to a publicly available dataset of the buffer layer FIB-SEM tomography measured by a team of researchers from University of Wisconsin at Madison and Oak Ridge National Laboratory. We evaluate the performance by applying mechanical modeling with problems of linear elastic homogenization and linear elastic brittle fracture material properties and comparing the behaviour of the dataset microstructure and the surrogate microstructure. This shows good agreement between the dataset microstructure and the generated microstructures over a large range of porosities. (10.1016/j.jnucmat.2026.156498)
  DOI : 10.1016/j.jnucmat.2026.156498