Stabilized non-ordinary state-based peridynamics with irregular nodal distribution

Abstract

Peridynamics is a nonlocal continuum mechanics model that is employed in fracture simulation, and its numerical applicability can be extended using irregular arrangements in the nodal distribution. This study investigates the effect of irregular grids on the numerical accuracy of stabilized non-ordinary state-based peridynamics to establish an appropriate range of peridynamic geometric parameters for irregular grids with geometrically nonlinear formulations. To this end, the peridynamic geometric parameters of irregular grids are estimated by interpolating a piecewise graph of the parameter versus the number of neighbor nodes in the regular grid. In addition, a direct tensile test is performed on a two-dimensional square plate, and the displacement results are compared with the analytical solution to determine the appropriate range of the geometric parameters. Using the parameter range, a large deflection of a beam is simulated in the explicit dynamic analysis. Overall, the results of the horizontal and vertical displacements are consistent with those obtained using the finite element method. The numerical models are verified to be generalizable for large displacements and rotations.