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

Theoretical analysis in the time-domain of wave reflection on cortical bone : generation on the lateral P-Wave.

National audienc

Réponse transitoire d'un bimatériau ; Application à un impact sur le thorax.

National audienc

Calculating of the exact response of a two-layered halfspace under dynamic point loading.

International audienc

Probabilistic modelling of an ultrasonic setup: calculation of the dispersion on wave speed measurements

International audienceThis Note presents a probabilistic model of transient wave reflection at a fluid-solid interface. The configuration represents an ultrasonic experiment used for bone tissue evaluation. The parametric method is used to derive the probabilistic model for the mechanical parameters of the solid (bone); the associated random variables are derived according to the maximum entropy principle. A Monte Carlo simulation, associated with the Cagniard-de Hoop method to calculate the acoustic response, yields the probability density for an output ultrasonic parameter similar to the velocity of longitudinal waves in the solid. Results demonstrate the sensitivity of the probability density of this parameter to the experimental setup

Elastoacoustic model with uncertain mechanical properties for ultrasonic wave velocity prediction: Application to cortical bone evaluation

International audienceThe axial transmission technique can measure the longitudinal wave velocity of an immersed solid. An elementary model of the technique is developed with a set of source and receivers placed in a semi-infinite fluid coupled at a plane interface with a semi-infinite solid. The acoustic fluid is homogeneous. The solid is homogeneous, isotropic, and linearly elastic. The work is focused on the prediction of the measured velocity (apparent velocity) when the solid is considered to have random material properties. The probability density functions of the random variables modeling each mechanical parameter of the solid are derived following the maximum entropy principle. Specific attention is paid to the modeling of Poisson's ratio so that the second-order moments of the velocities remain finite. The stochastic solver is based on a Monte Carlo numerical simulation and uses an exact semianalytic expression of the acoustic response derived with the Cagniard-de Hoop method. Results are presented for a solid with the material properties of cortical bone. The estimated mean values and confidence regions of the apparent velocity are presented for various dispersion levels of the random parameters. A sensibility analysis with respect to the source and receivers locations is presented

analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone

International audienc

Identification of the probabilistic model for a nonhomegeneous cortical bone using in vivo measurements in ultrasonic range

The uncertainties introduced in the construction of such a simplified model and the random nature of such a heterogeneous medium are taken into account in introducing a probabilistic model of the elasticity tensor of the cortical bone medium. This probabilistic model is then a non-Gaussian tensor-valued random field which is non-homogeneous in space, for which the mean field has a gradient in the thickness direction and for which the random fluctuations are defined by a spatial correlation length in the thickness direction and by a space dependent dispersion parameter controlling the level of the random fluctuations. The parameters which have to be identified by solving an inverse stochastic problem related to the wave propagation prediction model are then those relative to the mean value function of the random field, the correlation length and the dispersion function of the elasticity tensor random field of the cortical layer. The purpose is to present a method for this identification using experimental measurements in ultrasonic range