The classical approaches to modeling and simulation in solid mechanics rely heavily on constitutive models. These provide constitutive equations, which complement the balance equations of field, or boundary- value, problems. Extensive ongoing research effortsare devoted in the scientific community to tune and ever improve constitutive models and equations for various classes of materials and various regimes of solicitation (loading amplitudes and rates, temperature, chemistry, ...), as well as to identify associated parameters. Constitutive models thus present a very large diversity encompassing a wide range of applications, yet this variety also hints at the inherent epistemic uncertainty carried by these models. If the uncertainty associated to constitutive parameters can be quantified, the uncertainty associated to the models themselves is much more difficult to measure. From a more historical point of view, constitutive models were initially conceived to generalize experimental observations made on specific (typically homogeneous) loading regimes to more general loadings.

With the recent progress in imaging techniques, experimental observations are nowadays much richer in information and existing constitutive models are sometimes incompatible with this abundance of data. Data-driven approaches have recently been developed to better exploit the large volumes of modern experimental measures, while attempting to avoid the bias induced by constitutive models.

The present course will focus on a global data-driven approach, completely avoiding the use of models (statistical models or constitutive models), which could thus be labelled as model-free.

The proposed course will constitute a consistent and comprehensive introduction to the model-free data-driven paradigm for computational solid mechanics. After a general introduction to the data-driven paradigm, and how it fundamentally differs from the classical paradigm, the course will take students all the way from acquiring rich mechanical data sets, notably from imaging, to data-driven numerical simulation in nonlinear mechanics of structures. On the way, important aspects such as mathematical foundations of data-driven and machine learning methods, and the necessity and ways to account for the stochastic and imperfect nature of real-life data will be covered. Abundant data are also generated in multi-scale approaches, and the course will discuss how the data-driven paradigm may be relevant in that context as well. Finally, the current challenges in dealing with non- linearities and history-dependent behaviors will be discussed.

The course will also include a series of practical hands-on sessions, where the students will experiment with the data-driven approach, starting from a series of images from which to extract data, process it to construct a material database, and use this database in a data-driven simulation. It will also be shown how to couple data- driven algorithms with standard finite element software such as Abaqus.