Spatio-Trajectorial Optical Flow for Higher-Order Deformation Analysis in Solid Experimental Mechanics

Material models are required to solve continuum mechanical problems. These models contain parameters that are usually determined by application-specific test setups. In general, the theoretically developed models and, thus, the parameters to be determined become increasingly complex, e.g., incorporating higher-order motion derivatives, such as the strain or strain rate. Therefore, the strain rate behaviour needs to be extracted from experimental data. Using image data, the most-common way in solid experimental mechanics to do so is digital image correlation. Alternatively, optical flow methods, which allow an adaption to the underlying motion estimation problem, can be applied. In order to robustly estimate the strain rate fields, an optical flow approach implementing higher-order spatial and trajectorial regularisation is proposed. Compared to using a purely spatial variational approach of higher order, the proposed approach is capable of calculating more accurate displacement and strain rate fields. The procedure is finally demonstrated on experimental data of a shear cutting experiment, which exhibited complex deformation patterns under difficult optical conditions.