  We investigate quasistatic evolution in finite plasticity under the
assumption that the plastic strain is compatible. This assumption is
well-suited to describe the special case of dislocation-free plasticity and
entails that the plastic strain is the gradient of a plastic deformation map.
The total deformation can be then seen as the composition of a plastic and an
elastic deformation. This opens the way to an existence theory for the
quasistatic evolution problem featuring both Lagrangian and Eulerian variables.
A remarkable trait of the result is that it does not require second-order
gradients.
