SUMMARYThis paper deals with the identification of probabilistic models of the random coefficients in stochastic boundary value problems (SBVP). The data used in the identification correspond to measurements of the displacement field along the boundary of domains subjected to specified external forcing. Starting with a particular mathematical model for the mechanical behavior of the specimen, the unknown field to be identified is projected on an adapted functional basis such as a provided by a finite element discretization. For each set of measurements of the displacement field along the boundary, an inverse problem is formulated to calculate the corresponding optimal realization of the coefficients of the unknown random field on the adapted basis. Realizations of these coefficients are then used, in conjunction with the maximum likelihood principle, to set-up and solve an optimization problem for the estimation of the coefficients in a polynomial chaos representation of the parameters of the SBVP.

identification of the random elasticity field at mesoscale of a heterogeneous microstructure using multiscale experimental observations. International Journal for Multiscale Computational Engineering, Begell House, 2015, 13 (4), pp.281-295. 10.1615 Multiscale identification of the random elasticity field at mesoscale of a heterogeneous microstructure using multiscale experimental observations AbstractThis 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 tensorvalued 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

This paper deals with the experimental identification of the probabilistic representation of a random field modelling the Young modulus of a non homogeneous isotropic elastic medium by experimental vibration tests. Experimental data are constituted of frequency response functions on a given frequency band and for a set of observed degrees of freedom on the boundary of specimens. The random field representation is based on the polynomial chaos decomposition. The coefficients of the polynomial chaos are identified setting an inverse problem and then in solving an optimization problem related to the maximum likelihood principle.

The aim of this work is to evaluate the effect of a spatial gradient of material properties (mass density and stiffness coefficients) of cortical bone on its ultrasonic response obtained with an axial transmission device. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic solid layer sandwiched between two acoustic fluid layers and excited by an acoustic linear source located in one fluid layer, delivering broadband ultrasonic pulses. The model couples the acoustic propagation in both fluid media with the elastodynamic response of the solid layer. A constant spatial gradient of material properties is considered for two values of bone thicknesses corresponding to relatively thick and thin bone widths. For a thin bone (0.6 mm) compared to wavelength (around 4 mm at 1 MHz), the results are in good agreement with a S(0) Lamb wave assuming a homogeneous material with spatially averaged material properties. For a thick bone (4 mm), the results are in agreement with the propagation of a lateral wave and allow the derivation of an equivalent contributing depth in the case of a transverse isotropic inhomogeneous solid layer.