The interaction between cement and other constituents plays an important role in several engineering applications, such as in the construction and oil and gas (OandG) industries. In the construction industry, fiber-reinforced cementitious composites (FRC) have gained wide prominence for their excellent mechanical properties. Fibers can increase the post-cracking strength of the composite, improving concrete durability and controlling crack propagation in the cement matrix. Moreover, they perform a bridging mechanism at the interface, changing the material post-peak behavior. On the other hand, in the OandG industry, cement and steel are essential structural elements that should ensure well integrity and provide zonal isolation. This interaction is considered critical since a strong bond may prevent the generation of microannulus leakage paths along the cement and steel interface, which also can lead to crack propagation. In this sense, a comprehensive study of the damage mechanisms developed at the cement interface is essential in both applications to understand the material mechanical behavior. Therefore, it is possible to develop finite element models that consider the pullout mechanisms (debonding, adhesion, and friction) and the interface parameters that govern the local mechanical behavior of cement. While numerous experimental studies and numerical models exist, the current state-of-the-art lacks formulations investigating damage mapping and stress transfer interactions at the cement interface, particularly considering different cement matrix types and steel fiber geometries. This thesis addresses a critical gap in the literature by proposing the numerical modeling of interfacial debonding and damage evolution mechanisms for cement advanced materials and well integrity applications. Elastoplastic finite element models, incorporating surface-based cohesive formulations with contact, are employed to simulate cement interface behavior. Additionally, mechanical characterization tests and microCT analyses are conducted to validate and support the numerical model results, assessing shear strength and damage propagation at the cement interface. Therefore, this research can offer insights for engineers across disciplines to enhance mechanical performance and prototype new advanced materials by damage evolution investigation. The developed finite element models emerge as valuable tools for cost-effective evaluations of cement performance through reliably simulating pullout/pushout behavior.