Une stratégie de modélisation de matériaux à histoire pilotée par les données en mécanique numérique

Data-driven structural computation methods are gaining traction in solid mechanics, offering new ways to model material behavior beyond traditional constitutive laws. Early developments often minimized the role of Materials Science, but recent research has reintroduced physical meaning while keeping the benefits of data-driven formulations. These approaches have performed well in specific cases, yet nonlinear and complex materials remain challenging because high-quality experimental data are limited.This work presents a novel data-driven computational framework for materials with complex behavior, where experimental data are scarce and costly. The key idea is to replace classical constitutive equations with direct use of experimental data, maximizing the value of existing measurements. The method separates the governing equations into two sets: the equilibrium and compatibility equations, which remain unchanged, and the material behavior relations, now derived directly from data instead of mathematical models. The framework aims to be simple, extendable, and able to reduce computational costs, especially in multiscale simulations.To solve standard finite element problems within this framework, the approach uses the LATIN (LArge Time INcrement) method, an iterative strategy well established in nonlinear mechanics. Unlike conventional use, where constitutive equations are solved iteratively, the proposed method interpolates between experimental data points to determine the material state at each iteration.These data points form the Experimental Constitutive Manifold (ECM), a mathematical representation of the material's observed behavior. The ECM describes the state of the material using internal variables such as stress, strain, and hardening. However, some of these internal variables are hidden, as they cannot be directly measured in experiments. Determining these hidden variables is central to the method. Their calculation depends on Materials Science principles and forms the core contribution of this work.The determination of hidden variables is called the “Central Problem” of the ECM, a nonlinear, non-classical optimization problem aimed at reconstructing a complete and consistent ECM. Solving this problem enables the creation of comprehensive, unbiased material models that accurately reflect experimental data across the full domain of observation. The study presents the problem's mathematical formulation, a strategy for its resolution, and validation tools to assess ECM accuracy and robustness.Results show that interpolation between experimental points yields high accuracy even with limited data, demonstrating the practicality and efficiency of this approach in data-scarce contexts. Several examples, ranging from simple to complex cases, illustrate the method's ability to faithfully reproduce material behavior while minimizing modeling bias.Finally, the work identifies promising future directions, including extending the method to viscous behaviors and multiscale analyses. By combining the rigor of Materials Science with data-driven efficiency, this approach provides a solid foundation for next-generation material modeling that is both physically grounded and computationally adaptable.