Energy minimizing states in adhesion problems for elastic rods

In this paper we analyze and compare two different models for adhesion phenomena, recently proposed by the authors. In the first approach [9] a feasible expression of the adhesion energy is suggested by the existence problem of partially detached equilibrium states. In the second model [10] the macroscopic energy is obtained by performing a multiscale analysis and it is deduced via a macroscopic Γ-limit of the energy at the scale of the microstructure. Interestingly, we obtain that the first model can be deduced by the second one as the limit case when the parameter measuring the relative stiffness of the adhesive layer and the beam diverges.