Abstract
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).
Highlights
Within the framework of linear elasticity theory, the numerical modeling and simulation of heterogeneous materials with hierarchical complex random microstructure give rise to many scientific challenges
We present the results of the first single-objective optimization problem (21) at macroscale which consists in minimizing the macroscopic numerical indicator J macro ( a) constructed in the macroscopic domain of observation Ωmacro for identifying the optimal value amacro of a at obs macroscale
We have revisited the multiscale identification methodology recently proposed in Reference [140] for the mechanical characterization of the apparent elastic properties of a complex microstructure made up of a heterogeneous anisotropic material that can be considered as a random linear elastic medium within the framework of 3D linear elasticity theory
Summary
Within the framework of linear elasticity theory, the numerical modeling and simulation of heterogeneous materials with hierarchical complex random microstructure give rise to many scientific challenges Their modeling is a topical issue with numerous applications in diverse material sciences, including for instance sedimentary rocks, natural composites, fiber- or nano-reinforced composites, some concretes and cementitious materials, some porous media, some living biological tissues, among many others [1]. With the recent developments achieved around the construction of stochastic models for tensor-valued random elasticity fields and their experimental inverse identification using field imaging techniques, one of the most promising ways consists in introducing a prior stochastic model of the apparent elasticity tensor field of heterogeneous materials of the considered microstructure at a given mesoscale Note that this mesoscopic scale allows the introduction of the spatial correlation length(s) of the microstructure, and that for materials with a hierarchical structure, such as cortical bone or tendon, different mesoscopic scales can be defined. In the present probabilistic context, a major question concerns the statistical inverse identification of a prior stochastic model parameterized by a small or moderate number of hyperparameters using only partial and limited experimental data
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