In fracture mechanics, the tension compression asymmetry plays a crucial role in accurately describing crack initiation and propagation, as quasi-brittle materials typically resist compression while degrading under tension. Capturing this asymmetric behavior becomes particularly challenging for phase field approximations at finite strains. To be more precise, the extension of models designed for the geometrically linearized setting such as approaches based on a spectral decomposition of the strains or a volumetric-deviatoric decomposition to finite strains is not straight-forward. This work extends the no-tension approach introduced to the phase-field fracture community by De Lorenzis and Maurini (c.f. [1]) to finite strains. As a proof of concept, the extended formulation is applied to the cohesive fracture model developed by Lammen, Conti, and Mosler (c.f. [2, 3]). The results demonstrate improved adaptability and physical consistency in capturing the MCR effect compared to traditional methods.