Approximation and definition of state variables for a comprehensive description of damage for ceramic matrix composites

Over the past decades, non-linear models describing damage and fracture of architectured materials have highly progressed, taking into account varied scenarios of degradation under complex multi-axial loadings. Many of these models remain expansive to numericaly handle and difficult to understand. In parallel, full-field measurement has brought a large quantity of data. A challenging task for the researcher is extracting information from that data quantity. The extraction relies on state variables and the associated energetic potentials. This paper will present the automatic definition of state variables in two situations. The first situation corresponds to a local case where the objective is simplifying an existing constitutive relation. As an example, an anisotropic tensorial damage model developed is simplified to a scalar damage model. Several choices of approximations and errors will be discussed. The second situation corresponds to a structural case where the objective is to simplify fields. The developed point of view relies on local pattern extraction associated with a PUM/GFEM method. After the introduction of this method, an automatic building method is evaluated