Historically, contact analysis has been an important design tool for various applications such as vehicle crash analysis or manufacturing. It is also becoming increasingly more relevant in newer fields such compliant mechanism or metamaterial design. Even though contact has been a topic of discussion for decades, there are still challenges that need to be solved before a truly general contact analysis and optimization framework can be developed. As a milestone towards such framework, this project builds upon an existing novel linear contact analysis and a geometry immersion methodology developed in Interface-enriched Generalized Finite Element Method (IGFEM), to extend its capabilities to support large deformations (geometric non-linearities). Furthermore, a solution is presented to overcome void element over-stiffening in immersed large deformation contact analyses.