Energy dissipating properties of metamaterials have diverse industrial applications, e.g., mitigating damage under severe dynamic loading which include blast, impact, and seismic loading. These materials can prevent propagation of elastic waves in certain frequency ranges called bandgaps. Researchers have developed various novel internal geometrical configurations to create frequency bandgap, e.g., periodically arranged holes, locally resonant inclusions, and cracks. Metamaterials with periodically arranged holes exhibit pattern transformation under compressive load due to local elastic instability and absorbs elastic energy. Locally resonant metamaterials absorb energy through the phenomenon of local resonance. Cracks act as reflectors of elastic waves [1]. The combined effect of holes, inclusions, and cracks in metamaterials is not well studied. In this work, a class of metamaterials with a combination holes, inclusions, and cracks is studied to create frequency bandgaps. The idea is to use a combination of local buckling, local resonance, and wave reflection to enhance the bandgap and reduce wave amplitude. As these metamaterials involve discontinuities, classical continuum mechanics is not suitable to analyze them as it involves partial differential governing equations. Peridynamics (PD), being a nonlocal continuum theory, can handle discontinuities along with large deformations. We develop a finite deformation PD model to analyze these metamaterials. The PD model is validated with the experimental results furnished by Bertoldi et al. [2] and finite element results performed in ANSYS. Static and dynamic analyses are performed using the Newton-Raphson method and the Newmark-beta method, respectively. Wave propagation through various novel configurations is simulated, and the effect of microstructure on the bandgap is determined.