Experimental identification of mesoscopic elasticity tensor field for heterogeneous materials with complex microstructure using multiscale experimental imaging measurements
Résumé
The numerical modeling and simulation of heterogeneous materials with hierarchical complex microstructure (spanning several length scales) give rise to many scientific challenges occurring at various scales. Although such materials are often considered and modeled as deterministic homogeneous media at macroscale in most practical applications, they usually cannot be explicitly described by the local morphological and mechanical properties of their constituents at microscale. Nowadays, with the recent developments achieved around the construction of stochastic models for matrix-valued random tensor fields [1], one of the most promising way consists in introducing an ad hoc non-Gaussian stochastic model representing the apparent (random) elastic properties of heterogeneous materials for a representative volume element (RVE) subdomain defined at a given mesoscale (for which the usual assumption of scale separation in homogenization theories is not met). In this probabilistic context, a major question concerns the inverse identification of a prior stochastic model parameterized by a small number of hyperparameters using only partial and limited experimental data.
For this purpose, a general methodology has been recently proposed in [2] for the multiscale identification of (i) the tensor-valued random field modeling the apparent (random and heterogeneous) elasticity tensor field at a given mesoscale, and (ii) the effective (deterministic and homogeneous) elasticity tensor at macroscale. Such an experimental identification has been carried out by solving a challenging statistical inverse problem formulated as a multi-objective optimization problem with a cost function defined by three different indicators allowing some distances between the experimental measurements and the random solution of a stochastic boundary value problem (representative of the multiscale experimental configuration) to be quantified.
In this work, we present an improvement of the above methodology by introducing an additional mesoscopic indicator that allows replacing the global optimization (genetic) algorithm used in [2] with two alternative algorithms for a better computational efficiency and higher accuracy of the identification procedure. Finally, the proposed methodology is first validated on a “virtual material” (using multiscale simulated data obtained through numerical computations) and then exemplified on a real heterogeneous material (nodular graphite cast iron) (using multiscale experimental data obtained through mechanical
2 testing monitored by digital volume correlation) in both two- and three-dimensional cases.
References
[1] C. Soize. Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators. Computer Methods in Applied Mechanics and Engineering, 195(1–3):26–64, 2006.
[2] Manh-Tu Nguyen, Christophe Desceliers, Christian Soize, Jean-Marc Allain, and Hakim Gharbi. Multiscale identification of the random elasticity field at mesoscale of a heterogeneous microstructure using multiscale experimental observations. International Journal for Multiscale Computational Engineering, 13(4):281–295, 2015.