Documents published in Scipedia

• A coupled Multiscale Model of the Human Cornea Accounting for the Collagenous Microstructure and the Extracellular Matrix

  A. Pandolfi

  Complas2025.

  
  

  Abstract

  The human cornea is a complex, highly specialized structure necessary for the vision function of the Eye. The cornea, due to its shape and transparency, refracts and transmits the light to the retina. Cornea's mechanical properties, critical for maintaining corneal shape and function under intraocular pressure, arise from the composition of a hydrated proteoglycan-rich extracellular matrix (ECM) reinforced by an intricate network of collagen fibrils organized into lamellae. Despite extensive research, existing biomechanical models often fall short of capturing the coupled interplay between the ECM and collagen reinforcements, especially under physiological and pathological conditions. This work seeks to address this gap by proposing a novel computational model that integrates a continuum representation of the ECM with a discrete collagencrosslinking network. The continuum approach for the ECM is chosen to represent its viscoelastic behavior and interaction with fluid flow, critical for corneal hydration and load transmission. Conversely, the collagen network is modeled as a discrete, anisotropic reinforcement system, capturing the directional stiffness imparted by the collagen fibrils and their crosslinking. The model is developed to account for the influence of enzymatic degradation, age-related changes, and disease processes such as keratoconus, where alterations in the ECM-collagen coupling are known to drive structural instability.  The innovation of this approach lies in its multiscale integration, bridging the molecular mechanics of collagen crosslinking with macroscopic corneal behavior. By explicitly linking the continuum matrix with a collagen-reinforced network, the model offers some possibility to deepen our understanding of corneal mechanics.  The inclusion of experimentally derived parameters for collagen alignment, crosslink density, and ECM properties, will make the model predictive in the simulation of physiological responses to intraocular pressure and external mechanical perturbations.

  Abstract
  The human cornea is a complex, highly specialized structure necessary for the vision function of the Eye. The cornea, due to its shape and transparency, refracts and transmits [...]

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• Front tracking with a twist: the eXtreme mesh deformation approach (X-MESH)

  N. Moës

  Complas2025.

  
  

  Abstract

  The arbitrary Eulerian Lagrangian (ALE) formulation is a common approach for tracking fronts in finite element simulations. It is, however, difficult to track fronts over long distances because the mesh quality becomes poor on one side of the front. Moreover, traditional ALE front tracking cannot cope with changes in the front topology. To remedy the above problems (at least the first one), remeshing is required from time to time to maintain correct mesh approximation capability on both sides of the front. This remeshing requires projection of the field and updating of the database in the simulation, which is detrimental to the speed and accuracy. We introduce a new approach in which the set of nodes located on the front evolves over time allowing the front to migrate through the mesh. Topological changes are easily considered. For example, a front can nucleate, propagate and merge with other fronts as it propagates.  For the new approach to work properly, we must accept that some elements become very small and possibly of zero measure. This means that the elements can deform in extreme ways, hence the acronym X-MESH. Surprisingly, as we shall show, this situation does not prevent simulations from being carried out.   In short, X-MESH simply uses node movements to propagate fronts over long distances, even in the event of topological changes. The mesh topology remains unchanged during simulation. The size and sparsity of the finite element matrices are therefore fixed throughout the simulation, and no field projection is required. As the simulation progresses, nodes arrive and depart from the front. X-MESH's capability will be demonstrated for several important applications in mechanics and physics, such as front tracking in the Stefan phase change model or the simulation of immiscible two-phase flows. The work is funded by a European Research Council (ERC)  Synergy Grant whose co-pI is Professor J-F. Remacle also at UCLouvain

  Abstract
  The arbitrary Eulerian Lagrangian (ALE) formulation is a common approach for tracking fronts in finite element simulations. It is, however, difficult to track fronts over [...]

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• Recent developments in detecting and localizing weaknesses in structures for high-fidelity digital twins

  R. Lohner

  Complas2025.

  
  

  Abstract

  Given that all materials exposed to the environment and/or undergoing loads eventually age and fail, the task of trying to detect and localize weaknesses in structures is common to many fields. Traditionally, manual inspection was the only way of carrying out this task, aided by ultrasound, X-ray, or vibration analysis techniques. The advent of accurate, abundant and cheap sensors, together with detailed, high-fidelity computational models in an environment of digital twins has opened the possibility of enhancing and automating the detection and localization of weaknesses in structures. The procedures proposed here are based on measured forces and displacements/strains, and formulate the determination of material properties (or weaknesses) as an optimization problem for the strength factor. These procedures belong to the more general class of inverse problems where structural properties are sought based on a desired cost functional. The use of adjoint formulations and smoothing of gradients to quickly localize damaged regions makes the problem tractable. Recent developments include: extension to nonlinear materials, incorporation of uncertainty, and transient problems. Several examples show the viability, accuracy and efficiency of the proposed methodology and its potential use for high fidelity digital twins.

  Abstract
  Given that all materials exposed to the environment and/or undergoing loads eventually age and fail, the task of trying to detect and localize weaknesses in structures is [...]

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• AI-accelerated computational multiscale modeling

  D. Kochmann

  Complas2025.

  
  

  Abstract

  Multiscale modeling is the branch of computational mechanics that has suffered from the limits imposed by computational costs probably the most, owing to computations being performed on more than one scale. Consequently, the use of machine learning (ML) methods to bypass costly lower-scale or scale-bridging simulations has tremendous potential to accelerate multiscale modeling and provide new opportunities for simulating the complex mechanics of materials and structures. We will discuss a few recent applications of ML to the field of computational mechanics, all united by the ambition to accelerate simulations across scales. One example is ML-based surrogate material modeling to bypass expensive material point calculations, e.g., by using Recurrent Neural Operators (RNOs) as surrogates for computationally expensive constitutive laws. This is demonstrated for finite-strain crystal plasticity models for magnesium, which are typically too expensive to be used in a multiscale setting. Similarly, FE2 simulations can be considerably accelerated when replacing the microscale boundary value problem by an efficient ML-based surrogate model [1] – as we will show for multiscale simulations of beam-based metamaterials, accelerated by a Kolmogorov-Arnold (KAN) network. Another example are constitutive artificial neural networks for architected materials, which learn the complex constitutive response as a function of the underlying structural architecture [2] for use as surrogate models in macroscale boundary value problems. Overall, we demonstrate how the integration of the principles of mechanics and thermodynamics with ML tools can result in (sufficiently) accurate and efficient AIaccelerated solutions for computational multiscale modeling. We close by highlighting the potential of such tools also for design optimization, e.g., of architected materials.

  Abstract
  Multiscale modeling is the branch of computational mechanics that has suffered from the limits imposed by computational costs probably the most, owing to computations being [...]

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• Strain ageing phenomena in metallic alloys: Experiments and modelling

  S. Forest

  Complas2025.

  
  

  Abstract

  Static and dynamic strain ageing phenomena induced by the interaction between dislocations and solute atoms, are ubiquitous in engineering metallic alloys. In Nickel-based superalloys used for turbine disks in jet engines, negative strain rate sensitivity is observed at service tempature and results in the devlopment of Portevin-Le Chatelier bands. A viscoplastic constitutive model will be presented which captures the serrations in tensile notch samples and biaxial tension specimens. Finite element simulations then show the impact of DSA on the burst of turbine disks [1]. Static strain ageing is associated to the formation of L¨uders bands in steel sheets. We illustrate the impact of their propagation on the viscoplastic behaviour of zinc coatings on galvanized steel sheets, by means of crystal plasticity applied to zinc grains

  Abstract
  Static and dynamic strain ageing phenomena induced by the interaction between dislocations and solute atoms, are ubiquitous in engineering metallic alloys. In Nickel-based [...]

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• Variational Phase-Field Modeling of Fracture: Towards Second-Generation Models

  L. De Lorenzis

  Complas2025.

  
  

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• Recent advances in the development of reliable neural simulators based on graph architectures

  E. Cueto

  Complas2025.

  
  

  Abstract

  Of all the contributions that AI is making to computational mechanics, the possibility of developing learned simulators is one of the most interesting. Of course, there is a whole ecosystem of techniques that can be used for this purpose, but the use of geometric deep learning is perhaps one of the most promising. Of particular interest is the so-called graph neural network architecture, since traditional finite element meshes can themselves be considered a graph. Thus, it is very convenient to train such architectures with synthetic data obtained by high-fidelity simulation. As will be seen in our presentation, graph networks (possibly informed by physics) allow a very high degree of generalization, as well as the level of accuracy they provide.  In this talk we will show details about the inner workings of such networks, particularly the message passing scheme, and we will see how reliable they are for use in problems involving plasticity. 

  Abstract
  Of all the contributions that AI is making to computational mechanics, the possibility of developing learned simulators is one of the most interesting. Of course, there is [...]

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• Stability in Composite Bearing Structures within Room-and-Pillar Goafs under Repeated Mining

  W. Lv, L. Gao, Y. Wu, P. Xie, C. Lyu, R. You, T. Song, S. Li

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (3), 59

  
  

  Abstract

  During repeated mining of shallow and closely spaced coal seams, the failure of coal pillars within the upper goaf can induce dynamic hazards—such as shield jamming, support collapse, and roof fall—at the lower fully mechanized working face. To assess the stability of composite bearing structures, this study adopts a comprehensive approach that integrates orthogonal experimental design with single-factor experiments, supported by numerical simulation methods. Firstly, a composite bearing structure model is developed based on the engineering conditions of the Xingelao Coal Mine, followed by a comprehensive mechanical analysis. Secondly, experimental variables such as cement content, fly ash content, river sand content, and solid/slurry concentration are considered to systematically analyze their impact on backfill strength through proportion adjustment experiments. Furthermore, the controlled variable method is applied to adjust the backfill ratio, ultimately determining the optimal backfill mix ratio S8-2/3, which demonstrates a 7-day uniaxial compressive strength of 2.70 MPa with a backfill ratio of 2/3. This ratio satisfies both the mine’s strength requirements and cost-effectiveness criteria. Based on this, a failure model for the “backfill-pillar” composite bearing structure is established by integrating stress-strain curves with observed failure modes during load-bearing processes. Finally, numerical simulation software was utilized to perform a stability analysis on both the composite load-bearing structure formed by post-backfilling in the roomand-pillar goaf and the overlying strata of the mined-out area. Numerical simulation results indicate that, under repeated mining conditions, the use of S8-2/3 backfilling material in room-and-pillar goafs significantly enhances the load-bearing capacity of residual coal pillars. It also effectively controls overburden movement and supports the safe and efficient extraction of coal resources.OPEN ACCESS Received: 23/04/2025 Accepted: 16/06/2025 Published: 22/09/2025

  Abstract
  During repeated mining of shallow and closely spaced coal seams, the failure of coal pillars within the upper goaf can induce dynamic hazards—such as shield jamming, [...]

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• A Novel Analytical Framework for Investigating Mittag—Leffler Stability in Fractional Order Reaction—Diffusion Systems

  I. Bendib, A. Ouannas, M. Dalah

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (3), 58

  
  

  Abstract

  In this paper, we develop a novel analytical framework to investigate the Mittag-Leffler stability (MLS) of fractional order reaction—diffusion systems (FO-RDs). By employing fractional calculus and Lyapunov function (LF) techniques, we derive sufficient conditions that guarantee the system’s equilibrium point (EP) is reached within a settling time (ST). Our approach provides explicit estimates for the ST, linking the fractional dynamics to practical stability criteria. The theoretical results are rigorously validated through numerical simulations on a glycolysis RD model, which demonstrates rapid convergence of the state trajectories to the unique equilibrium. These findings not only deepen the understanding of the transient behavior in FO-RDs but also pave the way for applications in biomedical engineering, chemical reactor design, and environmental management, where swift stabilization is essential.OPEN ACCESS Received: 30/03/2025 Accepted: 17/06/2025 Published: 22/09/2025

  Abstract
  In this paper, we develop a novel analytical framework to investigate the Mittag-Leffler stability (MLS) of fractional order reaction—diffusion systems (FO-RDs). By [...]

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• Numerical Analysis of Protective Performance of Segmented Excavation Schemes for Metro Tunnels Considering Excavation-Induced Disturbance

  D. Lin, R. Lin, S. Zhou, H. Wang, Y. Xiao, J. Bao, L. Fei

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (3), 57

  
  

  Abstract

  This paper presents an integrated laboratory and numerical study on the effects of excavation-induced soil disturbance on the displacement of underlying metro tunnels, as well as the protective performance of different segmented excavation methods. Artificial disturbed soils were prepared by mixing salt grains and different cement contents into remolded Ningbo silty clay. One-dimensional compression tests and triaxial shear tests were then conducted. These tests were used to investigate and compare the engineering properties of undisturbed and artificially disturbed soils. Subsequently, the Hardening Soil Model with Small Strain (HSS) parameters were obtained for soils under varying degrees of disturbance. Considering the deterioration of soil properties due to disturbance and based on the disturbance zoning determined from the unloading influence depth and field measurements, numerical simulations were performed using Plaxis 3D. These simulations analyzed tunnel displacements induced by large-area direct excavation and three segmented excavation schemes. The results indicate that excavation-induced disturbance can significantly increase tunnel vertical displacement. Compared to unmitigated direct excavation, segmented excavation methods (i.e., block jumping excavation, ends to center excavation, and sequential excavation) can reduce the average tunnel displacement by about 28%. Among the three schemes, block jumping excavation offers the best balance between deformation control and efficiency with the highest comprehensive benefit index (11.04%). Ends to center excavation provides optimal deformation control but exhibits relatively low efficiency. In contrast, although sequential excavation effectively reduces displacement, it leads to concentrated deformation and low construction efficiency, making it the least favorable option.OPEN ACCESS Received: 13/04/2025 Accepted: 30/07/2025 Published: 22/09/2025

  Abstract
  This paper presents an integrated laboratory and numerical study on the effects of excavation-induced soil disturbance on the displacement of underlying metro tunnels, as [...]

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