  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).
