The investigation of stress transfer phenomena at the interface of composite materials has been a critical topic in mechanical engineering. This research examines the mechanisms governing the stress distribution at the interfaces and the exchange between different phases. Aiming at exploiting the complementary contributions of diverse materials within each phase, the analysis of bond behaviour could optimize the overall performance and functionality of composite materials. Numerous documents in literature provide efficient computational simulations that replicate the non-linear behaviour of interface contacts. However, many models are dependent on factors like grid-mesh configuration and step interaction. The purpose of this research is to develop an interface model, based on the elasto-plastic response of a single spring. The damage formulation includes contributions such as irreversible damage, plastic kinematic descriptors, and a hemivariational approach. Karush-Kuhn-Tucker conditions are derived to govern the evolution of descriptors, damage, and plastic variables. This model’s suitability and reliability are verified by comparing numerical results with experimental data from pull-out tests conducted on different systems of a single steel cord embedded in an inorganic mortar matrix. Finally, the evolution of damage and plasticity is also demonstrated.