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

Manh-Tu Nguyen 1 Christophe Desceliers 1 Christian Soize 1 Jean-Marc Allain 2 H. Gharbi 2
1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 LMS - Laboratoire de mécanique des solides
Abstract : This 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.
Keywords : Multiscale identification mesoscale random elasticity field heterogeneous microstructure multiscale experiments
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Manh-Tu Nguyen, Christophe Desceliers, Christian Soize, Jean-Marc Allain, H. Gharbi. Multiscale 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/IntJMultCompEng.2015011435⟩. ⟨hal-01162147⟩

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