  The quasistatic, Prandtl-Reuss perfect plasticity at small strains is
combined with a gradient, reversible (i.e. admitting healing) damage which
influences both the elastic moduli and the yield stress. Existence of weak
solutions of the resulted system of variational inequalities is proved by a
suitable fractional-step discretisation in time with guaranteed
numericalstability and convergence. After finite-element approximation, this
scheme is computationally implemented and illustrative 2-dimensional
simulations are performed. The model allows e.g. for application in geophysical
modelling of re-occurring rupture of lithospheric faults. Resulted incremental
problems are solved in MATLAB by quasi-Newton method to resolve
elastoplasticity component of the solution while damage component is obtained
by solution of a quadratic programming problem.
