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In this thesis, a simple law of adhesion with "digital" decohesion is proposed for modeling unilateral contact with adhesion, together with a stable experiment based on an original axisymmetric epoxy-stamp on glass-disc specimen for measuring the relevant adhesive properties. Both the digital law and the stable experiment are designed for overcoming the instability of the local decohesion process. The law features a digital (binary) decohesion drop without unloading (rather than a continuous decay with unloading). Otherwise, the law is "derived" from an adhesion energy and a decohesion dissipation function per unit interface area (which are not convex, yet dissipative for the later) as any standard generalized tribological law. The adhesion-decohesion properties of the law are the adhesive peak tension πn and the ultimate decohesion gap γn (producing twice the decohesion interface "energy" per unit area 2ω = πnγn). This adhesion-decohesion law is then mounted in parallel with the classical unilateral contact law. A new original axisymmetric specimen made of an epoxy stamp moulded on a glass (or another material) disc is designed and developed. Stability of the global decohesion process is mainly due to the axisymmetrical disc shape of the debonding interface crack, because the crack front perimeter and interface area increase with the crack radius and its square. Debonding stability is further augmented if the stamp base thickness increases with its radius, because the peak tension at the crack front then decreases as the crack radius increases. An optimally stable radial profile is proposed. Based on this specimen, a globally stable loading-unloading decohesion test is developed for measuring the relevant adhesive properties πn and γn or ω (in fact ω directly and πn and γn indirectly). The experiment is reproducible and the measures are accurate. The good agreement between numerical and experimental results confirms the validity of both the simple digital adhesion-decohesion law and the stable experiment with the new specimen. Finally, the robustness and versatility of the specimen to study adhesion are assessed by exploring many various tracks: adhesion between epoxy and different disc materials, stick-slip crack propagation, debonding stability under force control, stability with irregular initial crack, phenomenon of healing adhesion, possibility to use the optical methods in adhesion experiments and adhesion between different materials.