  The modeling of damage processes in materials constitutes an ill-posed
mathematical problem which manifests in mesh-dependent finite element results.
The loss of ellipticity of the discrete system of equations is counteracted by
regularization schemes of which the gradient enhancement of the strain energy
density is often used. In this contribution, we present an extension of the
efficient numerical treatment, which has been proposed in [1], to materials
that are subjected to large deformations. Along with the model derivation, we
present a technique for element erosion in the case of severely damaged
materials. Efficiency and robustness of our approach is demonstrated by two
numerical examples.
