Highly nonlinear solitary waves in periodic dimer granular chains

We investigate the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer and heavier beads (stainless steel) are alternated with softer and lighter ones (polytetrafluoroethylene beads). We find good agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously studied examples as special cases and also provides key insights into the influence of the dimer lattice on the properties (width and propagation speed) of the highly nonlinear wave solutions

Highly nonlinear solitary waves in heterogeneous periodic granular media

We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mass) cell structures in one-dimensional granular lattices. To vary the composition of the fundamental periodic units in the granular chains, we utilize beads of different materials (stainless steel, brass, glass, nylon, polytetrafluoroethylene, and rubber). This selection allows us to tailor the response of the system based on the masses, Poisson ratios, and elastic moduli of the components. For example, we examine dimer configurations with two types of heavy particles, two types of light particles, and alternating light and heavy particles. Employing a model with Hertzian interactions between adjacent beads, we find good agreement between experiments and numerical simulations. We also find good agreement between these results and a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments (dimer chains) and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of heterogeneous lattices on the properties (width and propagation speed) of the nonlinear wave solutions of this system

Modelling Chemical Vapour Infiltration in C/C composites: numerical tools based on µ-CT images

ISBN 978-3-00-032049-1International audienceIn the production of high-quality Ceramic-Matrix Composites, matrix preparation is often made by Chemical Vapor Infiltration (CVI), a process which involves many phenomena such as gas transport, chemical reactions, and structural evolution of the preform. Control and optimization of this high-tech process are demanding for modeling tools.In this context, a numerical simulation of CVI in complex 3D images, acquired e.g. by X-ray Computerized Microtomography, has been developed. The approach addresses the two length scales which are inherent to a composite with woven textile reinforcement (i.e. inter- and intra-bundle), with two numerical tools.The small-scale program allows direct simulation of CVI in small intra-bundle pores. Effective laws for porosity, surface and transport properties as infiltration proceeds are produced by averaging. They are an input for the next modeling step.The second code is a large-scale solver which accounts for the locally heterogeneous and anisotropic character of the pore space. Simulation of the infiltration of a whole composite material part is possible with this program.Validation of these tools on test cases, as well as some examples on actual materials, are shown and discussed

Analysis and Optimization of Stress Wave Propagation in Two-Dimensional Granular Crystals with Defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods

Modélisation numérique bi-échelle de l'infiltration chimique pour la préparation de composites à matrice céramique

International audienceNous présentons une méthode permettant de comparer les mérites respectifs de différents milieux poreux vis-à-vis de leur infiltrabilité, c'est-à-dire de leur capacité à se laisser infiltrer convenablement par des gaz réactifs suivant le procédé CVI (Chemical Vapor Infiltration). Grâce à des tomographies X à deux résolutions des échantillons à infiltrer et des outils de simulation d'infiltration déjà validés dans un autre contexte*, il a été possible de comparer ces deux milieux poreux avec des critères objectifs. Il en ressort que le milieu le mieux infiltrable n'est pas nécessairement celui qu'on peut imaginer intuitivement

Isothermal Chemical Vapor Infiltration Modeling by Random Walks in CMT 3D Images at Two Scales

International audienceThe production cycle of high-quality Ceramic-Matrix Composites (CMCs) often involves interphase or matrix deposition by Chemical Vapor Infiltration (CVI). This costly step has motivated many modeling approaches, in order to provide guidelines for process control and optimization. In this context, numerical tools for direct modeling of isothermal, isobaric CVI in complex 3D images of the composite architecture, acquired e.g. by X-ray Computerized Microtomography (CMT) have been developed. To address inter- and intra-bundle length scales inherent to a composite with a woven textile reinforcement, a numerical strategy has been set up, based on two numerical tools. They solve diffusion-reaction equations and handle simultaneously the progressive evolution of the porous structure. They involve distinct random walk methods and image handling routines. The small-scale program uses Pearson random walks simulating rarefied gas transport; the fluid/solid interface is explicitly represented as a set of triangles through a Simplified Marching Cube approach. Direct simulation of CVI in intra-bundle pores is possible with such a tool. Effective laws for the evolution of porosity, surface and transport properties as infiltration proceeds are inferred from these simulations by averaging and are considered as inputs for the next modelling step. The large-scale solver uses Brownian motion simulation; the porous medium is considered as a continuum with locally heterogeneous and anisotropic diffusivities, and the deposition reaction is handled through a survival probability computation. Simulation of the infiltration of a whole composite material part is possible with this program. Validation of these tools on test cases, as well as some examples on actual materials, are shown and discussed

Modelling Infiltration of Fibre Preforms From X-ray Tomography Data

12th INTERNATIONAL CERAMICS CONGRESS PART JInternational audienceThe production of high-quality Ceramic-Matrix Composites often includes matrix deposition by Chemical Vapour Infiltration (CVI), a process which involves many phenomena such as gas transport, chemical reactions, and structural evolution of the preform. Control and optimization of this high-tech process are demanding for modelling tools. In this context, a numerical simulation of CVI in complex 3D images, acquired e.g. by X-ray Computerized Microtomography, has been developed. The approach addresses the two length scales which are inherent to a composite with woven textile reinforcement (i.e. inter- and intra-bundle), with two numerical tools. The small-scale program allows direct simulation of CVI in small intra-bundle pores. Effective laws for porosity, internal surface area and transport properties as infiltration proceeds are produced by averaging. They are an input for the next modelling step. The second code is a large-scale solver which accounts for the locally heterogeneous and anisotropic character of the pore space. Simulation of the infiltration of a whole composite material part is possible with this program. Validation of these tools on test cases, as well as some examples on actual materials, are shown and discussed