CONCLUSIONS

The exact, fully consistent global stiffness matrix has been derived for a class of nonlocal isotropic damage models. Due to the long-distance interaction, the stiffness matrix has a larger bandwidth than for a local model and is in general nonsymmetric. Nonstandard contributions must be taken into account during the assembly procedure. Nevertheless, a fully consistent tangential stiffness matrix can be constructed and exploited in the global equilibrium iteration procedure.

The results indicate that the consistent nonlocal stiffness can reduce the total execution time of the incremental nonlinear analysis, especially when high accuracy is desired. Another possible area of application is the sensitivity analysis based on the exact linearization, which is an important ingredient of various optimization techniques.

For large-scale problems, especially in three dimensions, the performance of the incremental-iterative solution strategy is substantially increased by using an indirect, iterative solver, instead of a direct solver based on the factorization of the stiffness matrix. In the present study, the GMRES method with preconditioning by incomplete $LU$ decomposition has been successfully adopted.