This research proposes a shift from traditional constitutive modeling to a Data-Driven Computational Mechanics (DDCM) framework which has been recently introduced [1]. Instead of relying on complex constitutive equations, this approach utilizes a database of strain-stress states to model material behavior. The algorithm minimizes the distance between calculated mechanical states and database entries, ensuring compliance with equilibrium and compatibility conditions. This new paradigm aims to overcome the uncertainties and empirical challenges associated with conventional methods.

As a corollary tool for simulations DDCM, Data-Driven Identification (DDI) has emerged as a powerful standalone method for identifying material stress responses [2, 3]. It operates with minimal assumptions about while being model-free, this making it particularly suitable for calibrating complex models commonly used in industry.

Key objectives of this research include adapting DDCM strategies for plasticity [4] and fracture [5], enhancing DDI for high-performance computing, and evaluating constitutive equations. The proposed methodology involves collecting full-field measurement maps from an heterogeneous test, utilizing High-Speed cameras and Digital Image Correlation. It will adapt DDCM for ductile fracture scenarios, implement a DDI solver in a high-performance computing framework, and conduct an assessment of a legacy constitutive model without uncertainties. The focus will be on 316L steel, a material widely used in nuclear engineering.

This thesis is the result of a collaboration between several labs at CEA ans Centrale Nantes which are prominent in computational and experimental mechanics, applied mathematics, software engineering and signal processing.

[1] Kirchdoerfer, Trenton, and Michael Ortiz. 'Data-driven computational mechanics.' Computer Methods in Applied Mechanics and Engineering 304 (2016): 81-101.
[2] Leygue, Adrien, et al. 'Data-based derivation of material response.' Computer Methods in Applied Mechanics and Engineering 331 (2018): 184-196.
[3] Dalémat, Marie, et al. 'Measuring stress field without constitutive equation.' Mechanics of Materials 136 (2019): 103087.
[4] Pham D. et al, Tangent space Data Driven framework for elasto-plastic material behaviors, Finite Elements in Analysis and Design, Volume 216, 2023, https://doi.org/10.1016/j.finel.2022.103895.
[5] P. Carrara, L. De Lorenzis, L. Stainier, M. Ortiz, Data-driven fracture mechanics, Computer Methods in Applied Mechanics and Engineering, Volume 372, 2020, https://doi.org/10.1016/j.cma.2020.113390.