  In this paper, we introduce the notion of separately global solutions for
large-strain rate-independent systems, and we provide an existence result for a
model describing bulk damage. Our analysis covers non-convex energies blowing
up for extreme compressions, yields solutions excluding interpenetration of
matter, and allows to handle nonlinear couplings of the deformation and the
internal variable featuring both Eulerian and Lagrangian terms. In particular,
motivated by the theory developed in [49] in the small strain setting, and for
separately convex energies we provide a solution concept suitable for large
strain inelasticity.
