Inverse problems with the digital image correlation: approach and applications

Abstract

A viable approach to solve inverse problems in elasticity is proposed. It is based on regression algorithms to estimate materials and/or loading parameters by fitting the experimentally-evaluated displacement field to representative analytical solutions. Displacements are measured by the digital image correlation (DIC) technique and they are used as input for numerical procedures able to minimize the estimation errors of the unknowns and to quantify the unavoidable rigid body motions of the samples/components. In addition, thanks to ad-hoc developed iterative algorithms, non-linear phenomena related to high and localized stress/strain states, can be captured successfully. This latter represents a relevant novelty of the methodology as it allows to investigate plasticity-induced mechanisms in solid mechanics which are impossible to analyze with more traditional DIC-based approaches. Three different case studies are considered: 1) estimation of the stress intensity factor in fracture mechanics problems, 2) estimation of the elastic properties of a material by the Brazilian tests, 3) estimation of the contact pressure generated by thermally activated shape memory alloy (SMA) rings used for pipe coupling. The reliability and the accuracy of the method is demonstrated through systematic comparisons of the results with conventional techniques in experimental mechanics.