Robust Multiscale Identification of Apparent Elastic Properties at Mesoscale for Random Heterogeneous Materials with Multiscale Field Measurements

The aim of this work is to efficiently and robustly solve the statistical inverse problem related to the identification of the elastic properties at both macroscopic and mesoscopic scales of heterogeneous anisotropic materials with a complex microstructure that usually cannot be properly described in terms of their mechanical constituents at microscale. Within the context of linear elasticity theory, the apparent elasticity tensor field at a given mesoscale is modeled by a prior non-Gaussian tensor-valued random field. A general methodology using multiscale displacement field measurements simultaneously made at both macroscale and mesoscale has been recently proposed for the identification the hyperparameters of such a prior stochastic model by solving a multiscale statistical inverse problem using a stochastic computational model and some information from displacement fields at both macroscale and mesoscale. This paper contributes to the improvement of the computational efficiency, accuracy and robustness of such a method by introducing (i) a mesoscopic numerical indicator related to the spatial correlation length(s) of kinematic fields, allowing the time-consuming global optimization algorithm (genetic algorithm) used in a previous work to be replaced with a more efficient algorithm and (ii) an ad hoc stochastic representation of the hyperparameters involved in the prior stochastic model in order to enhance both the robustness and the precision of the statistical inverse identification method. Finally, the proposed improved method is first validated on in silico materials within the framework of 2D plane stress and 3D linear elasticity (using multiscale simulated data obtained through numerical computations) and then exemplified on a real heterogeneous biological material (beef cortical bone) within the framework of 2D plane stress linear elasticity (using multiscale experimental data obtained through mechanical testing monitored by digital image correlation)

A non-parametric probabilistic model for soil-structure interaction

International audienceThe paper investigates the effect of soil-structure interaction on the dynamic response of structures. A non-parametric probabilistic formulation for the modelling of an uncertain soil impedance is used to account for the usual lack of information on soil properties. Such a probabilistic model introduces the physical coupling stemming from the soil heterogeneity around the foundation. Considering this effect, even a symmetrical building displays a torsional motion when submitted to earthquake loading. The study focuses on a multi-story building modeled by using equivalent Timoshenko beam models which have different mass distributions. The probability density functions of the maximal internal forces and moments in a given building are estimated by Monte Carlo simulations. Some results on the stochastic modal analysis of the structure are also given

A time-domain method to solve transient elastic wave propagation in a multilayer medium with a hybrid spectral-finite element space approximation

International audienceThis paper introduces a new numerical hybrid method to simulate transient wave propagation in a multilayer semi-infinite medium, which can be fluid or solid, subjected to given transient loads. The medium is constituted of a finite number of unbounded layers with finite thicknesses. The method has a low numerical cost and is relatively straightforward to implement, as opposed to most available numerical techniques devoted to similar problems. The proposed method is based on a time-domain formulation associated with a 2D-space Fourier transform for the variables associated with the two infinite dimensions and uses a finite element approximation in the direction perpendicular to the layers. An illustration of the method is given for an elasto-acoustic wave propagation problem: a three-layer medium constituted of an elastic layer sandwiched between two acoustic fluid layers and excited by an acoustic line source located in one fluid layer

Multiscale identification of the random elasticity field at mesoscale of a heterogeneous microstructure using multiscale experimental observations

International audienceThis paper deals with a multiscale statistical inverse method for performing the experimental identification of the elastic properties of materials at macroscale and at mesoscale within the framework of a heterogeneous microstructure which is modeled by a random elastic media. New methods are required for carrying out such multiscale identification using experimental measurements of the displacement fields carried out at macroscale and at mesoscale with only a single specimen submitted to a given external load at macroscale. In this paper, for a heterogeneous microstructure, a new identification method is presented and formulated within the framework of the three-dimensional linear elasticity. It permits the identification of the effective elasticity tensor at macroscale, and the identification of the tensor-valued random field, which models the apparent elasticity field at mesoscale. A validation is presented first with simulated experiments using a numerical model based on the hypothesis of 2D-plane stresses. Then, we present the results given by the proposed identification procedure for experimental measurements obtained by digital image correlation (DIC) on cortical bone

Identification du modèle probabiliste de l'os cortical en utilisant des mesures expérimentales ultrasoniques in vivo

Cette communication présente une méthode permettant d'identifier, à partir de mesures ultrasoniques in vivo, le modèle probabiliste du tenseur d'élasticité de l'os cortical. La macrostructure même de l'os cortical est complexe et aléatoire en présence de pathologies telles que l'ostéoporose. De tels matériaux sortent du cadre des hypothèses des théories classiques de la porosité. La réponse transitoire ultrasonique de l'os est simulée avec un modèle simplifié pour lequel le tenseur d'élasticité est modélisé par un champ stochastique construit en utilisant le principe du maximum d'entropie

Experimental multiscale measurements for the mechanical identification of a cortical bone by digital image correlation

International audienceThe implementation of the experimental methodology by optical measurements of mechanical fields, the development of a test bench, the specimen preparation, the experimental measurements, and the digital image correlation (DIC) method, have already been the object of research in the context of biological materials. Nevertheless, in the framework of the experimental identification of a mesoscopic stochastic model of the random apparent elasticity field, measurements of one specimen is required at both the macroscopic scale and the mesoscopic scale under one single loading. The nature of the cortical bone induces some difficulties, as no single speckled pattern technique is available for simultaneously obtaining the displacement at the macroscopic scale and at the mesoscopic scale. In this paper, we present a multiscale experimental methodology based on (i) an experimental protocol for one specimen of a cortical bone, (ii) its measuring bench, (iii) optical field measurements by DIC method, (iv) the experimental results, and (v) the multiscale experimental identification by solving a statistical inverse problem

Dynamique non linéaire en déplacements finis des structures tridimensionnelles viscoélastiques en rotation

CHATENAY MALABRY-Ecole centrale (920192301) / SudocCLERMONT FD-IFMA (630142301) / SudocSudocFranceF

Nonlinear structural dynamics equations in finite displacements for three-dimensional viscoelastic rotating structures with cyclic symmetry and for small geometrical perturbations

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A modal strategy devoted to the hidden state variables method with large interfaces

International audienceIn many mechanical engineering applications, the interactions of a structure through its boundary is modelled by a dynamic boundary stiffness matrix. Nevertheless , it is well known that the solution of such computational model is very sensitive to the modelling uncertainties on the dynamic boundary stiffness matrix. In a recent work, the "hidden state variables method" is used to identify mass, stiffness and damping matrices associated with a given deterministic dynamic boundary stiffness matrix which can be constructed by using experimental measurements. Such an identification allows the construction of the probabilistic model of a random boundary stiffness matrix by substituting those identified mass, stiffness and damping matrices by random matrices. Nevertheless, the numerical cost of the "hidden state variables method" increases drastically with the dimension (number of degrees of freedom) of the interface. We then propose an enhanced approach which consists in a truncated spectral representation of the displacements on the boundary and with a partition of the frequency band of analysis. A collection of mass, stiffness and damping matrices is then identified for each sub-frequency band of analysis. A probabilis-tic model is constructed in substituting each of those matrices by random matrices. A numerical application is proposed