This study extends the ordinary state-based peridynamic theory by introducing the Mises yield criterion and linear isotropic strengthening model, establishing a numerical computational framework for peridynamic plastic constitutive modeling. A two-dimensional microstructural model of aluminum foam is created using a stochastic method, and simulations based on peridynamic computational programs are conducted to analyze the plastic deformation of aluminum foam with different porosities under impact and the propagation of cracks in the organic glass backboard. The results demonstrate that aluminum foam structures with higher porosities exhibit better impact resistance, with their plastic deformation capacity being a key factor. The simulation results are consistent with experimental data, confirming the accuracy of the simulations and the validity of the analytical conclusions. Furthermore, peridynamic methods effectively predict the propagation of cracks in the organic glass backboard and the initiation of interface cracks, further highlighting the advantages of high-porosity aluminum foam.