Robust identification of elastic properties using the Modified Constitutive Relation Error

The present study concerns the identification of linear elastic material properties based on inhomogeneous tests and the use of full-field measurements, often based upon inverse approaches. This study presents the formulation of the so-called Modified Constitutive Relation Error (MCRE) method in the context of elastostatics when dealing with uncertain data. Such an approach addresses the concept of the reliability of information and mainly consists in the partitioning of all the available mechanical quantities into a reliable set and a less reliable one, so as to take into account the measurement uncertainties and the error made on the constitutive equation into the formulation, and then allows to identify the sought material properties. The method is split in two steps: the first one consists in defining admissible mechanical fields from all the theoretical and experimental data, for a fixed set of mechanical properties. This is made by the minimization of a criterion allowing a compromise between the constitutive equation and the measurements adequacy. Then, the second step consists in the identification of the sought material properties and takes the form of minimizing a cost function defined by using the above admissible mechanical fields. A comparison with the Finite Element Model Updating (FEMU) method was performed on some numerical examples where realistic perturbations were added. This comparison showed that the MCRE method is more robust towards perturbations for similar input data. Moreover, the proposed method only deals with the available information and does not need additional hypotheses to calculate the mechanical quantities. Eventually, the method was applied to the identification of the shear modulus of an organic matrix composite from experimental data.