Stiffness parameter identification of planar structural element based on the Modified Constitutive Relation Error

Resumo

Visual inspection techniques for structural damage detection are inherently limited: damage can be concealed, too minor for visual detection, or situated in inaccessible areas such as the interior of a nuclear reactor. To overcome these challenges, model-based approaches grounded in the solution of inverse problems have gained prominence. In particular, finite element model updating using static or dynamic response data has emerged as a powerful strategy to identify and quantify damage. By calibrating numerical models to reflect observed structural behavior more accurately, these methods support more informed maintenance planning and targeted intervention. This study presents a numerical strategy for identifying the structural parameters of a steel plate by minimizing a modified Constitutive Relation Error (MCRE) functional. Starting from a reference measure, the method seeks admissible mechanical fields and localizes regions with high errors. Once this iterative step converges, parameter updating is initiated to estimate the material properties accurately. The MCRE framework is based on the partitioning of the governing equations into a reliable set—where all equations are strictly satisfied—and an unreliable set, which encompasses potential deviations in the constitutive law. In the first phase, the admissible fields are obtained solving the global balance equations using a quadratic energy function that respects both Neumann's and Dirichlet's boundary conditions. In the second phase, the material parameters are identified through the minimization of a cost function that incorporates the previously obtained admissible fields and the reference measures. The CASTEM open-source toolbox for finite element computation was chosen to implement MCRE algorithm. The results obtained in this study demonstrate that the proposed numerical strategy was effective in accurately identifying both the stiffness parameters and the location of the defect in the plate.