  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.
