A variable horizon method for coupling meshfree peridynamics to FEM

Peridynamics is a nonlocal reformulation of solid mechanics which can reproduce the solution of classical continuum mechanics as its horizon approaches zero. Taking this idea into consideration, we proposed a new coupling approach between meshfree peridynamics and finite element method. An intermediate variable horizon element called “morakkab” is introduced to transfer force and momentum between peridynamic and FEM regions. In the original peridynamic formulation, artificial ghost forces will arise if the horizon varies with position; The creation of these artifacts is avoided by utilizing a modified peridynamic equation of motion based on the concept of co-family. The accuracy of the method is illustrated in 2D benchmark tests. Using the modified equation of motion, compared to the original peridynamic formulation, dramatically decreases the relative errors with respect to the analytical solution.