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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.


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.,Paris West University Nanterre La Défense | Naili S.,CNRS Multiscale Modelling and Simulation Laboratory
Biomechanics and Modeling in Mechanobiology | Year: 2011

Speed of sound measurements are used clinically to assess bone strength. Trabecular bone is an attenuating composite material in which negative values of velocity dispersion have been measured; this behavior remaining poorly explained physically. The aim of this work is to describe the ultrasonic propagation in trabecular bone modeled by infinite cylinders immersed in a saturating matrix and to derive the physical determinants of velocity dispersion. An original homogenization model accounting for the coupling of independent scattering and absorption phenomena allows the computation of phase velocity and of dispersion while varying bone properties. The first step of the model consists in the computation of the attenuation coefficient at all frequencies. The second step of the model corresponds to the application of the general Kramers-Krönig relationship to derive the frequency dependence of phase velocity. The model predicts negative values of velocity dispersion in agreement with experimental results obtained in phantoms mimicking trabecular bone. In trabecular bone, only negative values of velocity dispersion are predicted by the model, which span within the range of values measured experimentally. However, the comparison of the present results with results obtained in Haiat et al. (J Acoust Soc Am 124:4047-4058, 2008) assuming multiple scattering indicates that accounting for multiple scattering phenomena leads to a better prediction of velocity dispersion in trabecular bone. © 2010 Springer-Verlag.


Clement A.,CNRS Multiscale Modelling and Simulation Laboratory | Soize C.,CNRS Multiscale Modelling and Simulation Laboratory | Yvonnet J.,CNRS Multiscale Modelling and Simulation Laboratory
International Journal for Numerical Methods in Engineering | Year: 2012

This paper is devoted to the computational nonlinear stochastic homogenization of a hyperelastic heterogeneous microstructure using a nonconcurrent multiscale approach. The geometry of the microstructure is random. The nonconcurrent multiscale approach for micro-macro nonlinear mechanics is extended to the stochastic case. Because the nonconcurrent multiscale approach is based on the use of a tensorial decomposition, which is then submitted to the curse of dimensionality, we perform an analysis with respect to the stochastic dimension. The technique uses a database describing the strain energy density function (potential) in both the macroscopic Cauchy green strain space and the geometrical random parameters domain. Each value of the potential is numerically computed by means of the FEM on an elementary cell whose geometry is given by the random parameters and the corresponding macroscopic strains being prescribed as boundary conditions. An interpolation scheme is finally introduced to obtain a continuous explicit form of the potential, which, by derivation, allows to evaluate the macroscopic stress and elastic tangent tensors during the macroscopic structural computations. Two numerical examples are presented. © 2012 John Wiley & Sons, Ltd.


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.


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.


Nguyen V.-H.,CNRS Multiscale Modelling and Simulation Laboratory | Naili S.,CNRS Multiscale Modelling and Simulation Laboratory
Computer Methods in Biomechanics and Biomedical Engineering | Year: 2013

This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally graded anisotropic material coupled with fluids. The viscous effects are taken into account. The geometrical configuration mimics the one of axial transmission technique used for evaluating the bone quality. We present a numerical procedure adapted for this purpose which is based on the spectral finite element method (FEM). By using a combined Laplace-Fourier transform, the vibroacoustic problem may be transformed into the frequency-wavenumber domain in which, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analysed using FEM. Several numerical tests are presented showing very good performance of the proposed approach. We present some results to study the influence of the frequency on the first arriving signal velocity in (visco)elastic bone plate. © 2013 Taylor & Francis.


Lemaire T.,CNRS Multiscale Modelling and Simulation Laboratory | Lemonnier S.,CNRS Multiscale Modelling and Simulation Laboratory | Naili S.,CNRS Multiscale Modelling and Simulation Laboratory
Biomechanics and Modeling in Mechanobiology | Year: 2012

The lacuno-canalicular permeability has been shown to play a key role in the behavior of bone tissue. The aim of this study is, by giving an overview of the determinations of this parameter, to question the paradoxical values provided by theoretical predictions and recent experimental measurements. We propose therefore a Kozeny-like law obtained by a numerical method which relates the permeability to the textural parameters of cortical bone microstructure. Moreover, we suggest possible explanations for this paradox considering the empirical difficulties and possible multiphysical effects. © 2011 Springer-Verlag.


Nguyen V.-H.,CNRS Multiscale Modelling and Simulation Laboratory | Lemaire T.,CNRS Multiscale Modelling and Simulation Laboratory | Naili S.,CNRS Multiscale Modelling and Simulation Laboratory
Biomechanics and Modeling in Mechanobiology | Year: 2011

It is well known that microcracks act as a stimulus for bone remodelling, initiating resorption by osteoclasts and new bone formation by osteoblasts. Moreover, microcracks are likely to alter the fluid flow and convective transport through the bone tissue. This paper proposes a quantitative evaluation of the strain-induced interstitial fluid velocities developing in osteons in presence of a microcrack in the interstitial bone tissue. Based on Biot theory in the low-frequency range, a poroelastic model is carried out to study the hydro-mechanical behaviour of cracked osteonal tissue. The finite element results show that the presence of a microcrack in the interstitial osteonal tissue may drastically reduce the fluid velocity inside the neighbouring osteons. This fluid inactive zone inside osteons can cover up to 10% of their surface. Consequently, the fluid environment of bone mechano-sensitive cells is locally modified. © 2011 Springer-Verlag.


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.

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