Authors: Marie Dalémat ¹; Michel Coret ¹; Adrien Leygue ¹; Erwan Verron ¹

• 1 Institut de Recherche en Génie Civil et Mécanique

Identifying the mechanical response of a material without presupposing any constitutive equation is possible thanks to the Data-Driven Identification algorithm developed by the authors. It allows to measure stresses from displacement fields and forces applied to a given structure; the peculiarity of the technique is the absence of underlying constitutive equation. In the case of real experiments, the algorithm has been successfully applied on a perforated elastomer sheet deformed under large strain. Displacements are gathered with Digital Image Correlation and net forces with a load cell. However, those real data are incomplete for two reasons: some displacement values, close to the edges or in a noise-affected area, are missing and the force information is incomplete with respect to the original DDI algorithm requirements. The present study proves that with appropriate data handling, stress fields can be identified in a robust manner. The solution relies on recovering those missing data in a way that no assumption, except the balance of linear momentum, has to be made. The influence of input parameters of the method is also discussed. The overall study is conducted on synthetic data: perfect and incomplete data are used to prove robustness of the proposed solutions. Therefore, the paper can be considered as a practical guide for implementing the DDI method.

• 1 HAL