An asymptotic strain-based formulation for isotropic damage with unilateral effects in thin adhesive layers

The mechanical response of adhesive joints is strongly influenced by damage mechanisms exhibiting tension–compression asymmetry, driven by the opening and closure of microcracks. In this work, a strain-based formulation for isotropic damage with unilateral effects is employed. The damage model is developed within a thermodynamically consistent framework with internal variables. Moreover, it provides a physically motivated representation of microcrack-induced degradation, incorporating recovery effects associated with crack closure and allowing for distinct responses under tensile and compressive loading conditions. The formulation is applied to a thin adhesive layer connecting two elastic adherents, and an asymptotic analysis is performed to derive an effective mechanical description of the damage evolution of the bonded joint. The predictive capabilities of the proposed approach are assessed through the analysis of a uniaxial test on a butt joint. The results highlight the role of unilateral effects in governing the global response, particularly in terms of stiffness degradation, damage evolution and the difference between tensile and compressive regimes.