Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis

Peridynamics is an effective method in computational solid mechanics for dealing with discontinuities. However, its computational cost limits its applications, especially when used in the most general form, non-ordinary state-based peridynamics. This paper considers two approaches which decrease the computational cost. The first approach accounts for symmetry boundary conditions in a peridynamic body. In nonlocal peridynamics, boundary conditions are applied to an area. Therefore, when modeling the symmetry boundary condition, assuming fixed particles around the symmetry axis yields incorrect results. The present formulation introduces constraints which allow modeling of local symmetry conditions. Second, the finite-element–peridynamic coupling method is adopted for non-ordinary state-based peridynamics. The coupling method enables the use of peridynamics around discontinuities like cracks, and the faster finite element for the surrounding body. These two methods effectively reduce the solution time with an acceptable accuracy. The validity of these approaches is studied through various examples. Also, ductile crack growth in a compact tension specimen is studied, applying the presented methods. Good agreement is found when comparing experimental results with corresponding numerical results obtained using either fully peridynamic or coupled models.