Strain analysis by a total generalized variation regularized optical flow model

Abstract

In this paper we deal with the important problem of estimating the local strain tensor from a sequence of micro-structural images realized during deformation tests of engineering materials. Since the strain tensor is defined via the Jacobian of the displacement field, we propose to compute the displacement field by a variational model which takes care of properties of the Jacobian of the displacement field. In particular we are interested in areas of high strain. The data term of our variational model relies on the brightness invariance property of the image sequence. As prior we choose the second order total generalized variation of the displacement field. This prior splits the Jacobian of the displacement field into a smooth and a non-smooth part. The latter reflects the material cracks. An additional constraint is incorporated to handle physical properties of the non-smooth part for tensile tests. We prove that the resulting convex model has a minimizer and show how a primal-dual method can be applied to find a minimizer. The corresponding algorithm has the advantage that the strain tensor is directly computed within the iteration process. Our algorithm is further equipped with a coarse-to-fine strategy to cope with larger displacements. Numerical examples with simulated and experimental data demonstrate the very good performance of our algorithm. In comparison to state-of-the-art engineering software for strain analysis our method can resolve local phenomena much better.Remark 7. The soft shrinkage (14) is obtained in the special case λ 1 = λ 2 andx 1 =x 2 .

Measurement of strain, strain rate and crack evolution in shear cutting

“…Due to the window-based approach it is impossible to resolve local phenomena good enough and results are often too smooth. Here, we propose to apply the variational model introduced by some of the authors in Balle et al (2019) for computing deformation and strain. In order to keep this paper self contained, we briefly sketch the method.…”

“…Therefore, the aim of this paper is to present an experimental setup for in situ strain and strain rate detection while maintaining the real-process boundary conditions. To this end, we also apply the optical flow approach with total generalized variation (TGV) prior introduced by Balle et al (2019) to resolve the crack initiation and propagation during shear cutting.…”

Crack Size Identification for Bearings Using an Adaptive Digital Twin

“…Different techniques, such as data-driven algorithms [ 3 ] and model-based methods [ 4 ], have been introduced to diagnose faults in bearings. The high resolution the optical flow approach with total generalized variation (TGV)-based optical approach for crack detection is introduced in [ 5 , 6 ]. The most important challenges of model-based methods are the increased complexity and decreased modeling accuracy in unknown conditions.…”

An Image Registration Model in Electron Backscatter Diffraction

“…In particular, optical flow models with priors containing higher order derivatives of the displacement field were successfully used, e.g., in [40,55,66,73,74]. In material science, such models were applied for the strain analysis in materials [10,36,38], where they appear to be more sensitive to abrupt changes in the displacement field than correlation based methods used in state-of-the-art software packages such as [16,24,25]. While optical flow models with a linearized data term as described above are mainly convex, nonconvex models have to be solved in registration [49,50], large deformation diffeomorphic metric mapping [12] or metamorphosis [72].…”