Finite strain formulation of the discrete equilibrium gap principle: application to direct parameter estimation from large full-fields measurements

The Equilibrium Gap Method (EGM) is a direct model parameter identification method, i.e., that does not require any resolution of the model. It has been extensively studied in the context of small strains but not thoroughly investigated for large strains. In this article, we propose a novel formulation of the EGM, valid in large strains, and applicable to both boundary and body forces, when full-field measurements are available. Our formulation is based on a recently proposed continuous formulation and consistent discretization of the equilibrium gap principle. Additionally, we developed an estimation pipeline to quantify the robustness of our new EGM formulation to noise, and we compared its performance to other classical estimation methods, namely the Finite Element Model Updating (FEMU) method and the Virtual Fields Method (VFM). Our robustness quantification pipeline involves generating synthetic data from a reference model through two methods: by adding noise to the reference displacement, or by generating noisy images and performing motion tracking with the Equilibrium Gap principle used as mechanical regularization. While the quality of estimation using our new EGM formulation is poor with the first data generation method, it improves drastically with the second method. Since the second method of synthetic data generation closely mimics experimental processes, the EGM, when combined with motion tracking with Equilibrium Gap regularization, demonstrates reasonable noise robustness. Thus, it is a promising option for direct parameter estimation from full-field measurements.