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Buonomo B.,The Second University of Naples | Manca O.,The Second University of Naples | Lauriat G.,CNRS Multiscale Modelling and Simulation Laboratory
International Journal of Thermal Sciences | Year: 2014

An analytic solution on fully developed forced convection, in parallel plates porous micro-channels is accomplished in Local Thermal Non-Equilibrium (LTNE) condition. The analysis is realized in steady state regime for rarefied gaseous slip flows between two parallel plates with assigned heat flux. The Darcy-Brinkman model is considered in the momentum equation and two energy equations are used to evaluate solid and fluid temperatures. The entropy generation analysis is performed and the total entropy generation number is evaluated as a function of the different dimensionless parameters. The effect of tangential momentum and thermal accommodation coefficients are examined. Results are reported in terms of average Nusselt numbers, dimensionless temperature profiles and total entropy generation number as a function of Biot number (Bi), effective thermal conductive ratio (κ), Darcy number (Da), accommodation coefficients (tangential momentum and thermal) and Knudsen number. Results show that heat transfer increases as Bi increases and reaches asymptotic values. Different trends are observed with respect to tangential momentum accommodation coefficient for assigned thermal accommodation. Total entropy generation number as a function of Da-0.5 presents minimum values with respect to Bi, accommodation coefficients and Brinkman number. © 2013 Elsevier Masson SAS. All rights reserved.

Soize C.,CNRS Multiscale Modelling and Simulation Laboratory | Poloskov I.E.,Perm State University
Computers and Mathematics with Applications | Year: 2012

Abstract The paper is devoted to the computational time-domain formulation of linear viscoelastic systems submitted to a nonstationary stochastic excitation and in the presence of model uncertainties which are modeled in the framework of the probability theory. The objective is to introduce and to develop an adapted and complete formulation of such a problem in the context of computational mechanics. A reduced-order model in the time domain with stochastic excitation is derived from the computational model. For the reduced-order model, the stochastic modeling of both computational model-parameter uncertainties and modeling errors is carried out using the nonparametric probabilistic approach and the random matrix theory. We present a new formulation of model uncertainties to construct the random operators for viscoelastic media. We then obtained a linear Stochastic Integro-Differential Equation (SIDE) with random operators and with a stochastic nonhomogeneous part (stochastic excitation). A time discretization of this SIDE is proposed. In a first step, the SIDE is transformed to a linear Itô Stochastic Differential Equation (ISDE) with random operators. Then the ISDE is discretized using an extension of the Störmer-Verlet scheme which is a particularly well adapted algorithm for long-time good behavior of the numerical solution. Finally, for the stochastic solver and statistical estimations of the random responses, we propose to use the Monte Carlo simulation for Gaussian and non-Gaussian excitations. © 2012 Elsevier Ltd. All rights reserved.

Haiat G.,CNRS Multiscale Modelling and Simulation Laboratory | Wang H.-L.,University of Michigan | Brunski J.,Stanford University | Brunski J.,Rensselaer Polytechnic Institute
Annual Review of Biomedical Engineering | Year: 2014

Dental implants have become a routinely used technique in dentistry for replacing teeth. However, risks of failure are still experienced and remain difficult to anticipate. Multiscale phenomena occurring around the implant interface determine the implant outcome.The aim of this review is to provide an understanding of the biomechanical behavior of the interface between a dental implant and the region of bone adjacent to it (the bone-implant interface) as a function of the interface's environment. First, we describe the determinants of implant stability in relation to the different multiscale simulation approaches used to model the evolution of the bone-implant interface. Then,we review the various aspects of osseointegration in relation to implant stability. Next, we describe the different approaches used in the literature to measure implant stability in vitro and in vivo. Last, we review various factors affecting the evolution of the bone-implant interface properties. Copyright © 2014 by Annual Reviews. All rights reserved.

Nguyen V.-H.,CNRS Multiscale Modelling and Simulation Laboratory | Naili S.,CNRS Multiscale Modelling and Simulation Laboratory
International Journal for Numerical Methods in Biomedical Engineering | Year: 2012

This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. © 2012 John Wiley & Sons, Ltd.

Rohan E.,University of West Bohemia | Naili S.,CNRS Multiscale Modelling and Simulation Laboratory | Cimrman R.,University of West Bohemia | Lemaire T.,CNRS Multiscale Modelling and Simulation Laboratory
Journal of the Mechanics and Physics of Solids | Year: 2012

In this paper, we develop a model of a homogenized fluid-saturated deformable porous medium. To account for the double porosity the Biot model is considered at the mesoscale with a scale-dependent permeability in compartments representing the second-level porosity. This model is treated by the homogenization procedure based on the asymptotic analysis of periodic microstructure. When passing to the limit, auxiliary microscopic problems are introduced, which provide the corrector basis functions that are needed to compute the effective material parameters. The macroscopic problem describes the deformation-induced Darcy flow in the primary porosities whereas the microflow in the double porosity is responsible for the fading memory effects via the macroscopic poro-visco-elastic constitutive law. For the homogenization procedure, we use the periodic unfolding method. We discuss also the stress and flow recovery at multiple scales characterizing the heterogeneous material. The model is proposed as a theoretical basis to describe compact bone behavior on multiple scales. © 2012 Elsevier Ltd. All rights reserved.

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