This study presents an ordinary state-based peridynamic (OSB PD) analysis within the finite-element framework while considering implicit/explicit solvers. The present PD formulation permits non-uniform discretization with a variable horizon and eliminates the use of external surface and volume correction factors. An implicit solver is employed until immediately before damage emerges, and then an adaptive time-stepping explicit solver for crack initiation and propagation. The major advantage of the present approach is the reduction in computational time. The PD interactions lead to a sparsely populated global stiffness matrix. The BiConjugate Gradient Stabilized (BICGSTAB) method is employed to determine the solution of the system equations. Damage onset and its evolution is investigated using the critical stretch criterion. The efficacy of the present approach is established by considering two different geometric configurations and loading/boundary conditions. The PD predictions for the crack patterns compare well with those of the analytical results and experimental observations.