  A novel finite element formulation for gradient-regularized damage models is
presented which allows for the robust, efficient, and mesh-independent
simulation of damage phenomena in engineering and biological materials. The
paper presents a Lagrange multiplier based mixed finite element formulation for
finite strains. Thereby, no numerical stabilization or penalty parameters are
required. On the other hand, no additional degrees of freedom appear for the
Lagrange multiplier which is achieved through a suitable FE-interpolation
scheme allowing for static condensation. In contrast to competitive approaches
from the literature with similar efficiency, the proposed formulation does not
require cross-element information and thus, a straightforward implementation
using standard element routine interfaces is enabled. Numerical tests show
mesh-independent solutions, robustness of the solution procedure for states of
severe damage and under cyclic loading conditions. It is demonstrated that the
computing time of the gradient damage calculations exceeds the one of purely
elastic computations only by an insignificant amount. Furthermore, an improved
convergence behavior compared to alternative approaches is shown.
