  We investigate numerically a quasi-static elasticity system of Kachanov-type.
To do so we propose an Euler time discretization combined with a suitable
finite elements scheme (FEM) to handle the discretization is space. We use
ODE-type arguments to prove the consistency of the scheme as well as its
convergence rate. We rely on the computational platform FEniCS to perform the
FEM discretizations in space needed to compute the model output. The simulation
results show a good agreement with both the physics of the problem and with our
previous qualitative mathematical analysis results obtained for precisely the
same problem setting. Furthermore, our implementation recovers nicely the
theoretically expected convergence rate. This is a preliminary study preparing
the framework for the rigorous numerical identification of the damage process
in Kachanov-type models.
