Evangéline Capiez-Lernout

Robust Design Optimization in Computational Mechanics

The motivation of this paper is to propose a methodology for analyzing the robust design optimization problem of complex dynamical systems excited by deterministic loads but taking into account model uncertainties and data uncertainties with an adapted nonparametric probabilistic approach, whereas only data uncertainties are generally considered in the literature by using a parametric probabilistic approach. The possible designs are represented by a numerical finite element model whose design parameters are deterministic and belong to an admissible set. The optimization problem is formulated for the stochastic system as the minimization of a cost function associated with the random response of the stochastic system including the variability of the stochastic system induced by uncertainties and the bias corresponding to the distance of the mean random response to a given target. The gradient and the Hessian of the cost function with respect to the design parameters are explicitly calculated. The complete theory and a numerical application are presented.

Blade Manufacturing Tolerances Definition for a Mistuned Industrial Bladed Disk

This paper deals with the characterization of the blade manufacturing geometric tolerances in order to get a given level of amplification in the forced response of a mistimed bladed-disk. The theory is based on the use of a nonparametric probabilistic model of blade random uncertainties, The dispersion parameters controlling the nonparametric model are estimated as a function of the geometric tolerances. The industrial application is devoted to the mistuning analysis of a 22 blades wide chord fan stage. Centrifugal stiffening due to rotational effects is also included. The results obtained validate the efficiency and the reliability of the method on three-dimensional bladed disks.

Nonparametric modeling of random uncertainties for dynamic response of mistuned bladed disks

The random character of blade mistuning is a motivation to construct probability models of random uncertainties. Recently, a new approach known as a nonparametric model of random uncertainties, based on the entropy optimization principle, was introduced for modeling random uncertainties in linear and nonlinear elastodynamics. This paper presents an extension of this nonparametric model for vibration analysis of structures with cyclic geometry. In particular this probability model allows the blade eigenfrequencies uncertainties and the blade-modal-shape uncertainties to be modeled.

What is the importance of multiphysical phenomena in bone remodelling signals expression? A multiscale perspective.

Cortical bone, constituting the outer shell of long bones, is continuously renewed by bone cells in response to daily stimuli. This process, known as bone remodelling, is essential for proper bone functioning in both physiological and pathological conditions. Classical bone remodelling models do not, or only implicitly do, take into account physico-chemical phenomena, focussing on the mechanosensitivity property of the tissue. The aim of this paper is to carry out an investigation of the multiphysical phenomena occuring in bone life. Using a recent multiscale model combining piezoelectricity and electrokinetics to poromechanics, the usual viewpoint of bone remodelling models is questioned and new research avenues are proposed.

A multiscale theoretical investigation of electric measurements in living bone : piezoelectricity and electrokinetics.

This paper presents a theoretical investigation of the multiphysical phenomena that govern cortical bone behaviour. Taking into account the piezoelectricity of the collagen–apatite matrix and the electrokinetics governing the interstitial fluid movement, we adopt a multiscale approach to derive a coupled poroelastic model of cortical tissue. Following how the phenomena propagate from the microscale to the tissue scale, we are able to determine the nature of macroscopically observed electric phenomena in bone.

Design Optimization With an Uncertain Vibroacoustic Model

This paper deals with the design optimization problem of a structural-acoustic system in the presence of uncertainties. The uncertain vibroacoustic numerical model is constructed by using a recent nonparametric probabilistic model, which takes into account model uncertainties and data uncertainties. The formulation of the design optimization problem includes the effect of uncertainties and consists in minimizing a cost function with respect to an admissible set of design parameters. The numerical application consists in designing an uncertain master structure in order to minimize the acoustic pressure in a coupled internal cavity, which is assumed to be deterministic and excited by an acoustic source. The results of the design optimization problem, solved with and without the uncertain numerical model, show significant differences.

Robust Updating of Uncertain Computational Models Using Experimental Modal Analysis

In this paper, a methodology is presented to perform the robust updating of complex uncertain dynamic systems with respect to modal experimental data in the context of structural dynamics. Because both model uncertainties and parameter uncertainties must be considered in the computational model, the uncertain computational model is constructed by using the nonparametric probabilistic approach. We present an extension to the probabilistic case of the input-error methodology for modal analysis adapted to the deterministic updating problem. It is shown that such an extension to the robust-updating context induces some conceptual difficulties and is not straightforward. The robust-updating formulation leads us to solve a mono-objective optimization problem in the presence of inequality probabilistic constraints. A numerical application is presented to show the efficiency of the proposed method.

Robust Analysis of Design in Vibration of Turbomachines

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. Robust analysis of design in vibration of turbomachines M. Mbaye, Christian Soize, J.-P. Ousty, Evangéline Capiez-Lernout

Properties of water confined in hydroxyapatite nanopores as derived from molecular dynamics simulations

Abstract Bone tissue is characterized by nanopores inside the collagen-apatite matrix where fluid can exist and flow. The description of the fluid flow within the bone has however mostly relied on a macroscopic continuum mechanical treatment of the system, and, for this reason, the role of these nanopores has been largely overlooked. However, neglecting the nanoscopic behaviour of fluid within the bone volume could result in large errors in the overall description of the dynamics of fluid. In this work, we have investigated the nanoscopic origin of fluid motion by conducting atomistic molecular dynamics simulations of water confined between two parallel surfaces of hydroxyapatite (HAP), which is the main mineral phase of mammalian bone. The polarizable core–shell interatomic potential model used in this work to simulate the HAP–water system has been extensively assessed with respect to ab initio calculations and experimental data. The structural (pair distribution functions), dynamical (self-diffusion coefficients) and transport (shear viscosity coefficients) properties of confined water have been computed as a function of the size of the nanopore and the temperature of the system. Analysis of the results shows that the dynamical and transport properties of water are significantly affected by the confinement, which is explained in terms of the layering of water on the surface of HAP as a consequence of the molecular interactions between the water molecules and the calcium and phosphate ions at the surface. Using molecular dynamics simulations, we have also computed the slip length of water on the surface of HAP, the value of which has never been reported before.

Water in hydroxyapatite nanopores: Possible implications for interstitial bone fluid flow

The role of bone water in the activity of this organ is essential in structuring apatite crystals, providing pathways for nutrients and waste involved in the metabolism of bone cells and participating in bone remodelling mechanotransduction. It is commonly accepted that bone presents three levels of porosity, namely the vasculature, the lacuno-canalicular system and the voids of the collagen-apatite matrix. Due to the observation of bound state of water at the latter level, the interstitial nanoscopic flow that may exist within these pores is classically neglected. The aim of this paper is to investigate the possibility to obtain a fluid flow at the nanoscale. That is why a molecular dynamics based analysis of a water-hydroxyapatite system is proposed to analyze the effect of water confinement on transport properties. The main result here is that free water can be observed inside hydroxyapatite pores of a few nanometers. This result would have strong implications in the multiscale treatment of the poromechanical behaviour of bone tissue. In particular, the mechanical properties of the bone matrix may be highly controlled by nanoscopic water diffusion and the classical idea that osteocytic activity is only regulated by bone fluid flow within the lacuno-canalicular system may be discussed again.