Multi-scale identification of composite using modified constitutive relation error: Formulation and numerical study

This paper investigates a new multi-scale approach, in which only one scale measurement is used to simultaneously identify the micro heterogeneous properties of composite at the measurement level and the macro homogeneous ones at the specimen level. Since the lack of information outside the measurement zone prevents identifying properties in this area, many multi-scale identification methods require at least two scales measurements. To resolve this problem, this paper proposes a multi-scale inverse identification strategy based on the principles of the Modified Constitutive Relation Error (M-CRE) using micro-scale full-field measurement. The basic idea is to construct mechanical fields and material parameters that are a trade-off between all available information, but with no further hypothesis. Two coupling schemes are proposed between the scales, and the reliability of the coupling equations is studied. We apply two steps to validate the multi-scale approach on numerical examples. Furthermore, the study of the measurement zone size effect and noise effect on the tension test illustrate the robustness of this multi-scale approach.