Stabilized coupling of non-ordinary state-based peridynamics and finite element method

Abstract

In the thesis, boundary effects that arise from crack surfaces and boundary conditions of the non-ordinary state-based peridynamics (NOSB-PD) model are identified and alleviated. Peridynamics is a non-local continuum mechanics developed for resolving difficulties in dealing with discontinuities such as cracks and voids. However, the boundary effect occurs due to the incomplete horizon near the boundaries and boundary conditions, which is a common issue in non-local numerical methods. To reduce the boundary effect, a quantitative stress treatment method is introduced at the crack front and surface and applied to δ- and m-convergence tests to narrow the variation of the crack paths. The stabilized coupling of NOSB-PD and finite element method is developed, and the boundary imposition method is implemented to reduce the boundary effect. The stabilized coupling model is verified through elastic and fracture problems. J2 plasticity theory is implemented and verified in the stabilized coupling model.