Quasistatic evolution of damage in an elastic body: numerical analysis and computational experiments

The processes of quasistatic evolution of the mechanical state of an elastic body, and the development of material damage which results from internal compression or tension, are modelled and numerically analyzed. The problem is formulated as an elliptic system for the displacements coupled with a parabolic equation for the damage field. The existence of the unique local weak solution is stated. Then, a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced. Finally, two two-dimensional numerical simulations are performed to show the accuracy of the scheme and the behaviour of the solution.