In this work, by making dimensionless the equations of the variational problem governing the wrinkling of Functionally Graded Material (FGM) membranes under tension, we highlight five dimensionless parameters that control the appearance and disappearance of wrinkles. These parameters are related to the aspect ratios, the properties of the FGM membrane, and the applied loading. The other two parameters are related to the properties of the FGM membrane which represent the ratio between the Young's moduli of the upper and lower surfaces of the FGM membrane, and p describes the variation of Young's modulus across the thickness of the FGM membrane. The fifth parameter is related to the imposed loading and the geometric and material characteristics of the membrane. For this purpose, we will use the full expression for thin- membrane deformation without approximating membrane effects, employing an extended F & ouml;ppl von K & aacute;rm & aacute;n (eFvK) model. The nonlinear equations will be solved numerically using the Asymptotic Numerical Method (ANM). Several numerical simulations are presented to study the effects of these dimensionless parameters on the appearance and disappearance of wrinkles.

In this research, we propose an algorithm to study the buckling of thin Functionally Graded Material (FGM) shells, utilizing a novel implementation of the asymptotic numerical method (ANM). Our approach integrates a three-step process: representation of variables and loading conditions through a truncated Taylor series, discretization using the finite element method (FEM), and advancement via a continuation method. This method is particularly effective for tracking the solution curve through systematic matrix inversion and tolerance adjustments. By applying this robust algorithm within the framework of Kirchhoff-Love theory, we analyze how the properties of FGM shells vary smoothly from metal at the base to ceramic at the surface, crucial for applications in aeronautics and civil engineering where stability under load is paramount. The results are validated against the Abaqus industrial code, demonstrating the accuracy of our model. Furthermore, we detail the impact of the volume fraction index on the load-displacement behavior and structural deformations, providing valuable insights for enhancing the design and safety of these critical structures.

In this work, a 3D micromechanical model is developed to describe the behavior of macromolecular chains and to reflect the hyperelastic behavior of rubber-like materials. This model generalizes the 2D model recently developed in Ouardi (2023). The behavior law is defined by the minimization of a potential energy, each macromolecular chain has been represented by elastic segments linked by nonlinear elastic spiral nodes. We thus obtain a model with only three characteristic parameters. We investigate, in the 3D case, the effect of the number of macro-chain segments and the shape of the Representative Volume Element (RVE) using a high-order algorithm of the family of the Asymptotic Numerical Method (ANM) (Cochelin, 2007). In the ANM algorithm, the solution of the nonlinear problem is sought branch by branch, each branch being represented by a Taylor series. In this way, this high-order algorithm makes it easier to continuously investigate the solution curves. Numerical simulations are presented on different RVEs, four and eight chains models (Arruda and Boyce, 1993), under three types of boundary conditions: uniaxial tension, pure shear and equibiaxial tension. These numerical simulations are compared with experimental data from Treloar (1944) to identify the parameters material and to demonstrate the robustness of the proposed model. The studied chains models show a slight influence of the number of macro-chains and the number of segments in the RVE.

Background: Nowadays, numerical algorithms make it possible to more accurately simulate the behavior of cardiac tissue, and in particular its electrical activity, in order to identify possible cardiac pathologies. Numerical methods used to simulate cardiac electrical activity, governed by unsteady non-linear PDEs, require very high computation times. Objective: In this paper, we propose a new numerical modeling of electrical activity in cardiac tissue using a new robust and rapid High-Order Implicit Algorithms (HOIAs) based on the Asymptotic Numerical Method (ANM) and meshless techniques. Methods: The numerical modeling is based on a time discretization, a homotopy transformation, a Taylor series representation, a meshless method and a continuation method. Two time steps are introduced: the first is directly linked to the scheme in time (small time step) and the second is linked to the continuation step (big time step). We develop three HOIA variants, using three meshless methods: Spectral Chebyshev Method, Radial Point Interpolation Method and Radial Basis Functions Method. Results and Conclusion : Using these three algorithms, in the case of the FitzHugh-Nagumo and Aliev- Panfilov ion kinetics models, we analyze the influence of algorithm parameters on CPU computation time and response quality. In this study, we will discuss the influence of the choice of the small time step on the big time step depending on the spatial discretization parameters, as well as the Asymptotic Numerical Method parameters (truncation order and precision parameter). The robustness, the efficiency and the utility of the proposed algorithms are demonstrated in the example of cardiac tissue in 2D case.

Estimation of contact patterns is often based on questionnaires and time-use data. The results obtained using these methods have been used extensively over the years and recently to predict the spread of the COVID-19 pandemic. They have also been used to test the effectiveness of non-pharmaceutical measures such as social distance. The latter is integrated into epidemiological models by multiplying contact matrices by control functions. We present a novel method that allows the integration of social distancing and other scenarios such as panic. Our method is based on a modified social force model. The model is calibrated using data relating to the movements of individuals and their interactions such as desired walking velocities and interpersonal distances as well as demographic data. We used the framework to assess contact patterns in different social contexts in Morocco. The estimated matrices are extremely assortative and exhibit patterns similar to those observed in other studies including the POLYMOD project. Our findings suggest social distancing would reduce the numbers of contacts by 95%. Further, we estimated the effect of panic on contact patterns, which indicated an increase in the number of contacts of 11%. This approach could be an alternative to questionnaire-based methods in the study of non-pharmaceutical measures and other specific scenarios such as rush hours. It also provides a substitute for estimating children’s contact patterns which are typically assessed through parental proxy reporting in surveys.

The understanding of crowd behavior dynamics holds immense significance in ensuring public safety across a range of situations, including emergency evacuations and large-scale events. Our research focuses on two primary objectives: investigating the impact of emotions on crowd movement and gaining valuable insights into collective behavior within crowds. To achieve this, we present a coupled model, incorporating an enhanced ASCRIBE model with an agent displacement model. We introduce heterogeneity into our model by incorporating specific mobility laws for different categories of panicked crowds, considering the influence of emotions on both speed and direction. Through numerical simulations, we analyze the model's parameters, observe the behavior of uniform crowds, and explore the collective dynamics within diverse crowds. By conducting comprehensive simulations and analyses, the findings from this study can contribute to the development of more effective crowd management strategies and emergency evacuation protocols.

In this work, we focus on the wrinkling phenomenon of Functionally Graded Material (FGM) membranes under uniaxial tensile traction using the Asymptotic Numerical Method (ANM). The objective of this study is to use a comprehensive model based on the Föppl-von Kármán theory. The obtained non-linear equations are solved using the ANM algorithm, aiming to numerically demonstrate the influence of FGM parameters, thickness, material parameter and aspect ratio on determining the critical wrinkling load and post-critical behavior. A comparison between the results obtained by ANM and those of Abaqus is presented.

Emotions play a major role in crowd dynamics, especially in panic situations where the consequences of emotional contagion can be disastrous. In order to reduce negative emotional contagion, the paper aims to investigate factors influencing the spread of panic in a crowd. Indeed, a mathematical approach based on the solicitation-response (action-reaction) principle is presented to describe crowd emotional intensity including personality traits. To capture important influential factors in the emotional contagion process, we assess the impact of domain quality, crowd distribution, density, and emotional state heterogeneity on the emotional contagion rate. Numerical simulations highlight many emotional states that can occur in a panic situation, as well as interventions to calm the crowd down; besides low densities and distancing measures, optimal configurations combined with human barriers would reduce the number of panicked agents and contain emotional agitation. The proposed study can allow the development of decision support tools for dealing with crowd panic situations.

In this article, we show that the reduced model proposed in our recent article to study the wrinkling of homogeneous elastic membranes does not reproduce the wrinkling observed in the case of an FGM-type composite membrane. New reduced models are then proposed to investigate the wrinkling of membranes made from Functionally Graded Materials (FGM). We examine, by this way, the influence of material functional parameters on determining the critical load and post-critical behavior under different loads. These reduced models, created using a multi-scale method based on Fourier series with slowly varying coefficients, enrich the reference model. In addition, these reduced models also allow us to significantly decrease the computation time and the number of finite elements compared to the complete model. The robustness of these reduced models is demonstrated in the case of wrinkling of membranes modeled by very thin shells, which are discretized using DKT18-type finite elements as described in literature. The resulting nonlinear problems are solved using a High-Order Continuation Method (HOCM).

In this work, we propose a new model based on a micromechanical approach for modeling the behavior of macromolecular polymer chains. We propose to consider that the segments of the Kuhn chain are deformable and that there is a bending stiffness between these segments. This modeling allows to find the classical S-shaped response curves.

In this work, we propose a microstructurally motivated hyperelastic model to describe the behavior of rubber-like materials. At the scale of the Representative Volume Element (RVE), we assume that, for each macromolecular chain, the segments of the chains are deformable and that there is a bending energy between two consecutive segments. We propose to model each macromolecular chain using micro-mechanical elements: elastic bars to represent the segments between cross-linking points and elastic spire to illustrate the flexibility of rotations around the cross-linking points. We thus suggest to model the behavior of the macrochain, using a quadratic spring like potential for a linear behavior of the chain segments, associated with a nonlinear elastic sigmoidal behavior at the connection points between Kuhn segments. Numerical simulation, on different RVEs, show that the proposed modeling represent the response of hyperelastic rubber-like materials in uniaxial extension, simple shear, pure shear and biaxial extension. In order to validate the proposed model, the results obtained in the case of four RVEs will be compared with the experimental data of Treloar (1944). These comparisons show that the proposed model is able to reproduce the experimental behavior of rubber-like materials.

In this work we propose a microstructurally motivated hyperelastic model to describe the behavior of elastomer materials. At the scale of the Representative Volume Element (RVE), composed of randomly oriented macromolecular chains, we assume that the segments of the chains are deformable and that there is a bending energy between two consecutive segments. We propose to model each macromolecular chain using micromechanical elements: linear elastic bars to represent the segments between the cross-linking points and non linear elastic spires to represent the flexibility of rotations around the cross-linking points. Numerical simulations, on different structured RVEs composed of 3, 4, and 8 chains in the case of three boundary conditions: uniaxial compressible tension, uniaxial incompressible tension, and shear, show that this modeling allows to find the classical response curves of hyperelastic elastomeric. In the proposed model, we have to identify only three parameters: a, $$ M_0 $$ and K. From numerical simulations, we show that the first parameter, a, control the first phase of activation of rotations between chain segments, the second parameter, $$ M_0 $$ , control the unfolding phase, and that the third parameter K control the stiffening phase at large deformations.

In this study, we present a new high-order implicit algorithm to simulate cardiac electrophysiological waves. Several cardiac pathologies are due to a malfunction in the propagation of the wave causing the contraction of the heart: the cardiac action potential. Its dynamics are described by a system of nonlinear and nonstationary partial differential equations (EDP). However, these equations retain major challenges for numerical simulation. These challenges are mainly reflected in the coexistence of a slow dynamic and a rapid dynamic inducing abrupt changes in time and space and having a wavefront type behavior. Faced with these challenges, we propose in this work an algorithm belonging to the family of asymptotic numerical methods (ANM), which combines representations in whole series, implicit time schemes, a mesh-less approach to spatial discretization using radial base functions (RBF) and a continuation method. This combination improves accuracy and significantly reduces computation time. To demonstrate its effectiveness, we first apply the algorithm to a one-dimensional equation (1D) of Fisher flame propagation, then to a two-dimensional equation (2D) modeling cardiac electrical activity, especially the well-known FitzHugh-Nagumo.

During infectious disease outbreaks, some infected individuals may spread the disease widely and amplify risks in the community. People whose daily activities bring them in close proximity to many others can unknowingly become superspreaders. The use of contact tracking based on social networks, GPS, or mobile tracking data can help to identify superspreaders and break the chain of transmission. We propose a model that aims at providing insight into risk factors of superspreading events. Here, we use a social force model to estimate the superspreading potential of individuals walking in a bidirectional corridor. First, we applied the model to identify parameters that favor exposure to an infectious person in scattered crowds. We find that low walking speed and high body mass both increase the expected number of close exposures. Panic events exacerbate the risks while social distancing reduces both the number and duration of close encounters. Further, in dense crowds, pedestrians interact more and cannot easily maintain the social distance between them. The number of exposures increases with the density of person in the corridor. The study of movements reveals that individuals walking toward the center of the corridor tend to rotate and zigzag more than those walking along the edges, and thus have higher risks of superspreading. The corridor model can be applied to designing risk reduction measures for specific high volume venues, including transit stations, stadiums, and schools.

ABSTRACT The evolution of mechanical properties of NR with carbon black fillers was examined after a thermal aging step through both experimentation and non-deterministic numerical simulations. A quantification of mechanical properties and associated variability is first proposed for a set of specimens exposed at different temperatures and exposure times. Second, a family of stretch–stress laws is numerically built with a James' hyperelastic model. Next, the whole of the behavior evolution is modeled with a Kriging model to quantify the effects of properties on a macroscopic stiffness, useful in dynamic simulations, and the least-favorable scenario is so determined. Finally, Arrhenius method is performed to numerically draw the evolution bounds of macroscopic stiffness as a function of aging exposure, followed by a comparison with a naturally aged suspension component. To our knowledge, the methodology developed has not already been proposed in this area.

In this paper we investigate the modeling of chemo-physical evolution due to thermo-mechanical loadings at finite strain in soft materials. In particular we discuss the question of a proper and consistent thermodynamical formulation in the case of nearly incompressible materials. The objective of this phenomenological modeling is to represent the thermo–chemo-mechanical aging that occurs in filled rubbers during high-cycle fatigue for some specific loading conditions.

Transport industry and, more specifically, railway industry, is confronted with a permanent need of improvement of its products. The competitiveness of rolling stock does not come only from low-cost production, but also from wise-calculated lifecycle costs. Nowadays, many contracts for railway operators include not only rolling stock, but also its maintenance services throughout its lifetime, which may reach up to 30% of global costs. Hence, deep knowledge about the system’s ageing is a strong asset to ensure a good performance, both on quality of service and financial costs. Rubber parts are widely used in railway technology because of their mechanical properties, providing both stiffness and, to a certain extent, additional damping and vibration filtering. Unlike metallic parts, whose mechanical properties remain relatively stable, rubber’s behaviour can change throughout a lifecycle, due to service loads and environmental influence. Such changes might have an impact on the system’s overall behaviour and lead to undesirable scenarii. For a given bogie model, we seek to estimate the stiffness variation of some rubber parts, which are deemed critical for safe operation.