H. Gharbi

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

The 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.

Stochastic representations and statistical inverse identification for uncertainty quantification in computational mechanics

The paper deals with the statistical inverse problem for the identification of a non-Gaussian tensor-valued random field in high stochastic dimension. Such a random field can represent the parameter of a boundary value problem (BVP). The available experimental data, which correspond to observations, can be partial and limited. A general methodology and some algorithms are presented including some adapted stochastic representations for the non-Gaussian tensor-valued random fields and some ensembles of prior algebraic stochastic models for such random fields and the corresponding generators. Three illustrations are presented: (i) the stochastic modeling and the identification of track irregularities for dynamics of high-speed trains, (ii) a stochastic continuum modeling of random interphases from atomistic simulations for a polymer nanocomposite, and (iii) a multiscale experimental identification of the stochastic model of a heterogeneous random medium at mesoscale for mechanical characterization of a human cortical bone.