Speaker: Nour Hachem

Date: Thursday 3rd of December 2026, 1:15pm

Abstract:

The Data-Driven Identification (DDI) method estimates the mechanical response of material samples without assuming a predefined constitutive model. DDI solves an inverse problem based on the principle that similar strains should correspond to similar stresses, while ensuring mechanical equilibrium. This work focuses on the development and theoretical validation of the DDI method. First, a rigorous mathematical and numerical analysis is provided, including the study of the uniqueness criterion, a new implementation with a proof of convergence, and an assessment of conditioning and convergence rates. Second, the case of ill-posed DDI problems is addressed, and corrective strategies are introduced to obtain valid solutions. Finally, essential tools and practical guidelines for reliable implementation are developed, providing a reference for future research and applications. These contributions establish a rigorous theoretical foundation for the DDI method, enhancing its robustness and applicability while enabling safer use through essential tools and a clearer understanding of its practical limitations.