Cohesive zone elements (CZE) are widely utilized for modeling fracture and delamination problems. Typically, a traction-separation law is employed to represent the interface between two continuous domains in these models. The simplicity of these models has made them a preferred approach for addressing such problems, leading to extensive research aimed at improving their accuracy and enhancing their performance. In this study, we propose a numerical method that significantly reduces the computational burden often associated with modeling fracture behavior. We incorporate global enrichment functions into 2D domains of beam models, leveraging pre-existing analytical knowledge about the global behavior of the system. The enrichment functions are introduced through the eXtended\Generalized Finite Element Method (XFEM\GFEM), utilizing the beams' natural vibration modes. Additionally, we enrich the interfaces by employing an enriched displacement field for the cohesive zone finite elements in their longitudinal direction. The proposed approach is implemented to solve classical problems in fracture mechanics in which the behavior is dominated by bending of beams with cohesive interfaces. The results demonstrate that this approach substantially reduces computational effort without a significant loss in solution accuracy.