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.
Highlights
Optical techniques have been used over a time-scale of more than one century as powerful non-contact tools to determine the mechanical properties of materials
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
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
Summary
Optical techniques have been used over a time-scale of more than one century as powerful non-contact tools to determine the mechanical properties of materials. The methodology is based on DIC measurement of the displacement field experienced by a sample during a thermo-mechanical test and the application of the regression methods to calculate unknown parameters such as material constants and/or external loads. Thanks to iterative calculation algorithms plasticity-induced non-linear effects, can be captured successfully minimizing the estimation errors This latter represents an important aspect of the methodology as it allows to account for important mechanisms in structural mechanics that are impossible to capture with more traditional DIC-based methods. The methodology was applied to three case studies with the aim to evaluate: i) the stress intensity factor on fracture mechanics problems, ii) the elastic properties of a material by means of Brazilian test, iii) the contact pressure generated by thermally activated shape memory alloy (SMA) rings used for pipe coupling [49]. Results revealed that this latter represents a viable technique for materials/components characterization
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