This work involves the characterization of effective thermal conductivity of polymer aerogel reinforced by graphene and graphene oxide elaborated by replacing the liquid phase with a gas phase through an environmentally friendly freeze-drying process. For characterizing the developed aerogel, multiscale geometrical configurations were constructed based on the experimental characterizations of the prepared aerogels. Following that, a homogenization procedure was applied, moving from smaller to larger scales. At the nanoscale, the Milton method was used, while at the micro- and macroscales, the asymptotic method was employed in combination with the finite element method. Problems posed on a domain called the representative unit cell were formulated at both micro- and macroscales, and their resolution using the finite element method allows the calculation of characteristic functions of the problems, thereby obtaining effective thermal conductivity of the material. To the best of our knowledge, no studies have been reported in the literature on the multiscale characterization of the effective properties of polymer aerogels, hence the motivation for this work. To address this gap, a novel numerical approach has been developed to investigate aerogel properties across multiple scales. The multiscale approaches have revealed the influence of various microstructural characteristics on the effective thermal conductivity properties of the hybrid aerogel. The results show that graphene and graphene oxide nanoinclusions do not significantly affect the thermal conductivity, but they do significantly improve the mechanical properties of the polymer-based aerogel. Furthermore, this study has also demonstrated that aerogels with superinsulating properties can be obtained by reducing the pore size to the nanometer scale and lowering the gas pressure to below 0.01 atm.

In this work, we presents a novel approach for predicting the effective properties of composite materials by integrating multiscale homogenization techniques with deep learning. High-fidelity datasets are generated using Milton's method and asymptotic homogenization through finite element simulations, capturing material behavior across scales from the nanoscale to the macroscale. A key contribution of this study is the development of an advanced multiscale homogenization model that accounts for heterogeneous property distributions within the representative volume element at the mesoscale, enabling more realistic and accurate material representation. The generated datasets are used to train multilayer perceptron models that achieve high predictive accuracy and strong generalization across both similar and dissimilar inclusion scenarios, while significantly reducing computational cost compared to conventional methods for predicting the effective properties of composite materials, specifically the effective thermal conductivity of hybrid aerogels. Additionally, the surrogate models show strong extrapolation capability, providing physically consistent predictions beyond the training domain. This scalable and robust framework offers a powerful tool for data-driven material design and can be readily extended to predict other effective properties.

We consider elastodynamics in periodically heterogeneous solids described by 1D continua.The homogenization based on the higher order asymptotic expansions is applied to derive effective (macroscopic) models.Relevance of these models is extended beyond the assumption of the perfect scale separation to respect finite size of the heterogeneities.These models involve higher order gradients enabling to interpret models of the generalized continua introduced using phenomenological approaches.Particular examples of bi-and triple-layered periodic composites are explored in the context of the wave dispersion analysis.It appears that a variety of models which approximate the response up to the 2 nd order of accuracy with respect to the scale parameter can be used, leading to different dispersion properties.Due to the volume forces involved in the asymptotic analysis, structures with resonators can be represented to enhance band gap effects.

This work reports on numerical characterizations of effective mechanical properties associated with graphene-polymer composite aerogels produced using an environmentally friendly freeze-drying process. To this purpose, a multiscale approach was implemented, in which geometrical configurations were constructed based on the results of experimental characterizations. A homogenization procedure based on molecular mechanics, the Milton method, and the asymptotic homogenization method was applied. In the asymptotic homogenization method, cell problems were formulated and solved within a representative volume element using the finite element method. After validating the numerical model through experimental results from compression tests, a parametric study on the influence of microstructural parameters of the materials, such as dispersion state, aspect ratio, volume fraction of nanoinclusions, and material porosity, on the macroscopic mechanical behavior of the composite aerogels was conducted. The simulation results provided a deeper understanding of the mechanisms that enhanced the mechanical properties of such aerogels by adding various graphene derivatives, allowing for adjustments in the elaboration process to obtain materials with improved mechanical properties.

This paper is a multi-aspect study which has undertaken essential numerical characterizations of not only mechanical and hydraulic properties but also acoustic behaviour of a new bio-based porous epoxy resin obtained by a ?green? adapted combination of the cationic photopolymerization and the porogen leaching technique. This new kind of material generally possesses interconnected fillet-edge cubic pores which lead to more complex morphology than in the case of spherical or cylindrical pores. In order to characterize the effective properties of the material, a multiscale approach using the asymptotic homogenization method has been applied. Such a method has induced cell problems whose resolutions have been conducted on the geometrical configuration defined from the experimental data of the samples by using scanning electron microscopy (SEM) and mercury intrusion porosimetry (MIP). The sound absorption behaviour of a plate made of the studied material has been subsequently characterized by solving a normal incidence acoustic problem with an assumption of rigid impervious backing. The mechanical model has been validated by balancing numerical results of the sound absorption coefficient, reflection coefficient, surface impedance, equivalent dynamic density and equivalent dynamic bulk modulus with corresponding experimental results obtained by conducting the three-microphone impedance tube testing. As a consequence, the mechanical model has been applied to investigate the influence of microstructural characteristics on effective properties and acoustic performance of the material. To the authors? knowledge, the features of the microstructure obtained from an elaboration process using the porogen leaching technique have rarely been studied in the literature. Four types of ordered pore arrangements together with systematic variations of the porosity and the pore size have been taken under consideration. Based on the results of these investigations, the subtle relation between microstructures and properties has been established. The processing parameters of material elaboration could be adjusted so that the obtained porous material would possess the best sound absorption performance.

This paper has carried out numerical characterizations of effective thermal properties of a new kind of macroporous bio-based epoxy resin. This new kind of material was synthesized by a free-solvent and free-amine-hardener process combining the cationic photopolymerization and the solid porogen leaching technique. In order to determine the effective thermal properties of the material, the asymptotic homogenization method has been used, deriving a cell problem from microscopic thermal equations. By solving this problem on a representative volume element consisting of elementary fillet-edge cubic pore and matrix which have been idealized from experimental pore characterizations, the effective thermal conductivity and diffusivity tensors have been attained. The asymptotic homogenization method revealed the effect of microstructural characteristics via pore arrangements, porosity and pore size on the effective thermal properties of the porous material. This first stage in the material development allows to propose adjustments in the elaboration process to improve the thermal insulation characteristics of a biosourced epoxy resin with two porosity levels. The paper has also provided examples of multilayer walls using the studied epoxy resins as thermally insulating materials. These walls including two or three insulation layers with different thicknesses have been assumed to suffer either a step change or a harmonic variation of the temperature at one side of the walls. Transient thermal responses of multilayer walls to the above thermal excitations have been dealt with by a semi-analytical approach in the context of one-dimension problems.

The integration between soft and hard materials often occurs through functionally graded interphases, which are typically designed as multilayers whose material properties gradually vary in space, in order to reduce mechanical stresses. In the musculoskeletal system in particular, the attachment between tendon and bone occurs through a specific functionally graded interphase called enthesis, which serves the challenging task of connecting these two highly dissimilar tissues over a very small region by means of finely tuned gradients in structure, composition and biomechanical properties at different length scales. Current computational models that aim at mimicking the biomechanical behavior of the tendon-to-bone complex at the organ scale generally fail in incorporating the impact of the microstructure across the interphase because of computational burden. In this study, we propose a modeling strategy that allows replacing the finite heterogeneous functionally graded interphase by an equivalent model with specific interface conditions. This can be achieved by enriching the equivalent interface model with proper forms of surface kinetic and potential energy densities, in order to retain the mechanics from the microstructure for a certain range of validity. The performance of this model is evaluated in the context of quantitative ultrasound, by comparing the calculated power reflection coefficient to that obtained using different baselines. The results show that our enriched model provides an accurate approximation of the reference interphase model over a broad frequency range, thus opening new perspectives for developing more sophisticated dynamic models targeting characterization or reattachment procedures at the organ scale. Number

Despite the unique mechanical strength and adhesion properties of epoxy resins, they still suffer from poor toughness and brittleness inducing poor resistance to cracks. Herein, we report an efficient method of synthesis of bioepoxy resin nanocomposites filled with highly exfoliated epoxy-grafted montmorillonite. The filled resin network was produced by covalent incorporation of a binary nanocomposite (MMT-PGMA) synthesized via in situ photoinduced polymerization of glycidyl methacrylate, into a Bioepoxy resin matrix to design a ternary nanocomposite (MMT-PGMA/Bioepoxy) and this in the presence of a green polyamine used as curing agent. The materials structure and morphology were characterized by FTIR, TGA, XRD, SEM, and TEM which show the key role of the MMT surface modification on its interfacial adhesion with the epoxy resin. The results showed that the clay interlayer d-spacing increases from 1.23 nm to more than 2.2 nm upon grafting of the polymer. The homogeneous solvent-free dispersion of hybrid clay nanofillers, via sonication process, enhanced remarkably the bioepoxy resin glass transition temperature (T-g) by 26.5 degrees C. This can be rationalized by both the nanofillers fine dispersion and the chemical surface reactivity ensuring strong interfacial adhesion with the matrix.

This paper deals with the development of a computational model to predict transient elastic waves in fluid-structure multilayer systems for which the elasticity constants of the structure are uncertain. The fluid-structure system is a three layers system make up of an elastic solid layer sandwiched between two acoustic fluid layers and excited by an acoustic line source located in one of the two acoustic fluid layers. The mean model of the elastic solid layer is represented by a transverse isotropic material. The elasticity tensor of the solid layer is modeled by a random tensor for which the probabilistic model is constructed using the information theory. A Monte Carlo stochastic numerical solver is used in order to solve the stochastic boundary value problem. A numerical application is presented.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Probabilistic model of human cortical bones with uncertain mechanical properties: Modelling and identification with experimental measurements in ultrasonic range Christophe Desceliers, Christian Soize, S. Naili, Q. Grimal, M. Talmant

This paper aims to study the dispersion phenomena of acoustic waves propagating in a periodic poroelastic medium. At mesoscale, the poroelastic saturated media is modeled by using Biot theory. We will compare two computational procedures for estimating the effective phase velocities and attenuation of plane waves in the period poroelastic structure at the macroscopic scale. First, wave-based Bloch analysis was employed to derive a finite element formulation which yields a quadratic complex eigenvalue problem. The equivalent fast/slow compressional and shear wave modes may be recognized by analyzing the computed complex wave numbers. Second, we used the asymptotic homogenization method to derive the poroelastic and dynamic permeabilities properties of an effective poroelastic model which allows us to estimate the effective wave dispersion. The polarization of wave modes at the cell level may be reconstructed from macroscopic solution. Numerical results show that both methods could provide well-matched estimations of the effective phase velocities and attenuation within the first Brillouin zone associated with the periodic structure

The characterization of the interphase condition between two materials is current in mechanics. In general, its modeling is achieved by considering an interface with only purely elastic properties. In this paper, following previous works, also inertial interface properties are taken into account. For sufficiently low-frequency regime, we investigate two density profiles (affine and quadratic), for the interphase. Moreover, the interface and the interphase are placed between two solids with different characteristics. The first one is non-dispersive, while for the second one three cases are considered: (a) solid without microstructure, i.e., a Cauchy continuum, (b) solid with microstructure characterized by normal dispersion, i.e., a strain gradient continuum, and (c) by anomalous dispersion. The reflection coefficients are plotted for each case. These results are evaluated with respect to a benchmark finite elements simulation of the finite heterogeneous interphase, and the error is discussed. It is shown that the effects of microstructure can be appreciated at higher frequencies and that the proposed model results to be accurate.

On approaches, methods and problems related to wave dispersion in porous media E. Rohan, V.-H. Nguyen, V. Lukeš, R. Cimrman, S. Naili NTIS – New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Univerzitnı́ 8, 301 00 Plzeň, Czech Republic Laboratoire Modélisation et Simulation Multi Echelle, Université Paris Est Creteil,MSME UMR 8208 CNRS, Créteil cedex, France