A classical continuum mechanics fails in case of discontinuity. Some investigations have shown that for complex damage and fracture processes like crack propagation, delamination and other phenomena, the application of classical fracture mechanics is just limited possible and leads to incorrect prediction. The significance of long-range forces in the nature of the damage was also examined. A number of methods were developed to predict the damage behavior, like XFEM, cohesive theory, phase-field method and also some applications of molecular dynamics. Peridynamics (PD) is a continues non-local approach containing a length scale. Nevertheless, peridynamics is computationally expensive in comparison to finite element method (FEM). In addition, there are difficulties in applying the initial and boundary conditions because of the non-local character of the theory. Some coupling techniques of PD with the FEM have already been developed to reduce or avoid such problems. A certain amount of them was proposed to apply only for static problems. We consider different coupling strategies: A Partitioned Coupling framework [1] and Arlequin based Penalty Coupling [2] and compared according to the following criterions: computational costs, convergence to the local solution, difficulties of choosing specific numerical parameters. The dynamic behavior is investigated as well. REFERENCES [1] Y. Yu, F.F. Bargos, H. You et. al.: A Partitioned Coupling Framework for Peridynamics and Classical Theory: Analysis and Simulations, Computer Methods in Applied Mechanics and Engineering, 2018, https://doi.org/10.1016/j.cma.2018.06.008 [2] Pernatii, A., Gabbert, U., Naumenko, K., Hesse, J.-T., Willberg, C.: A penalty method for coupling of Finite-Element and Peridynamic models, Proceedings in Applied Mathematics and Mechanics, 6 October 2022.