A LATIN-PGD reduced order approximation dedicated to the solution of an optimal control based identification strategy for non-linear constitutive parameters

Abstract

The objective of the research is to obtain deterministic identification of non-linear material parameters from full field measurements of kinematic data acquired from digital image correlation (DIC). The inverse problem involves proposal of the optimal control approach, considered to be a variant of modified constitutive relation error (MCRE), where the complete knowledge of the boundary conditions and the measurement data are not required. The optimisation problem essentially translates into minimisation of a quadratic functional under non-linear constraints. The non-linear optimisation is solved through the iterative large time increment (LATIN) method. A proper generalised decomposition (PGD) based reduced order approximation is also incorporated in this procedure for the sake of numerical frugality of the iterative method. Finally, a few numerical examples are depicted that establish the efficacy of the methodology.