Model and mesh selection from a mCRE functional in the context of parameter identification with full-field measurements.

In this paper, we propose a general deterministic framework to question the relevance, assess the quality, and ultimately choose the features (in terms of model class and discretization mesh) of the employed computational mechanics model when performing parameter identification. The goal is to exploit both modeling and data at best, with optimized model accuracy and computational cost governed by the richness of available experimental information. Using the modified Constitutive Relation Error concept based on reliability of information and the construction of optimal admissible fields, we define rigorous quantitative error indicators that point out individual sources of error contained in the identified computational model with regards to (noisy) observations. An associated adaptive strategy is then proposed to automatically select, among a hierarchical list with increasing complexity, some parameterized mathematical model and finite element mesh which are consistent with the content of experimental data. In addition, the approach is computationally enhanced by the complementary use of model reduction techniques and specific nonlinear solvers. We focus here on experimental information given by full-field kinematic measurements, e.g. obtained by means of digital image correlation techniques, even though the proposed strategy would also apply to sparser data. The performance of the approach is analyzed and validated on several numerical experiments dealing with anisotropic linear elasticity or nonlinear elastoplastic models, and using synthetic or real observations.