Computation and visualization of local deformation for multiphase metallic materials by infimal convolution of TV-type functionals

Abstract

Estimating the local strain tensor from a sequence of microstructural images, realized during a tensile test of an engineering material, is a challenging problem. In this paper we propose to compute the strain tensor from image sequences acquired during tensile tests with increasing forces in horizontal direction by a variational optical flow model. To separate the global displacement during insitu tensile testing, which can be roughly approximated by a plane, from the local displacement we use an infimal convolution regularization consisting of first and second order terms. We apply a primal-dual method to find a minimizer of the energy function. This approach has the advantage that the strain tensor is directly computed within the algorithm and no additional derivative of the displacement must be computed. The algorithm is equipped with a coarse-to-fine strategy to cope with larger displacements and an adaptive parameter choice. Numerical examples with simulated and experimental data demonstrate the advantageous performance of our algorithm.