Non-contact reconstitution of the traction distribution using incomplete deformation measurements: Methodology and experimental validation

Traction distribution is often unknown in solid mechanics. However, identifying traction distribution with both high accuracy and spatial resolution can sometimes be critical. In this paper, we consider the frequent situation where incomplete deformation measurements, such as partial surface measurements obtained by digital image correlation, are available. For such situations, we propose to achieve the complete identification of boundary tractions, using an optimization based inverse method. The feasibility and robustness of the proposed approach are firstly assessed with numerical simulations. We show that complete traction distributions can be identified with high accuracy even when there is noise added to the deformation measurements. More specifically, the relative error was less than 3% even with 10% noise. Moreover, the effect of noise depends significantly on the level of incompleteness of the deformation data. We show for instance that when the measurement area is 8.3% of the solid, the relative error can be 5 times larger than when the measurement area is 33.3%. However, even with 8.3% deformation measurement area of the solid, the relative error of the mapped traction distribution can be less than 6%. Besides, the accuracy of the mapped traction distribution can be further improved if the region of the deformation measurement is closer to the traction boundary. We eventually validate the proposed inverse approach using incomplete experimental datasets consisting in tensile tests carried out on two elastic samples. We obtain very promising results, with relative errors below 4% using the measured displacements of only 3 points, which is promising to open potential applications in different fields of engineering.