A Cell Method Stress Analysis in Thin Floor Tiles Subjected to Temperature Variation

The Cell Method is applied in order to model the debonding mechanism in ceramic floor tiles subjected to positive thermal variation. The causes of thermal debonding, very usual in radiant heat floors, have not been fully clarified at the moment. There exist only a few simplified analytical approaches that assimilate this problem to an eccentric tile compression, but these approaches introduce axial forces that, in reality, do not exist. In our work we have abandoned the simplified closed form solution in favor of a numerical solution, which models the interaction between tiles and sub-base more realistically, when the positive thermal variation increases the volume of the sub-base. The thermal problem has been approached as a contact problem in a composite structure. In particular, the kinematic and equilibrium conditions have been imposed at the interface between lower part, which is the sub-base, and the upper part, which is composed by the adhesive, the tiles, and the grouting between the tiles. The failure condition has been studied in the Mohr-Coulomb plane by using the Leon criterion, a unifying criterion that combines the shear stress with traction and compression. Therefore, we employed a unique failure criterion both for the nodes at the interface between sub-base and adhesive (which undergo a shear/tensile failure or a shear failure) and the nodes at the interface between tiles and grouting (which undergo a tensile failure). This allowed us to model the tile debonding both in the horizontal and in the vertical interfaces, while previous FEM codes treated the tile debonding only on the horizontal interfaces. The numerical analyses were performed in parametric modality, by varying the geometric and mechanical characteristics of the model. Particular attention was devoted to the modeling of thin tiles, a new type of ceramic tiles, for which there are no yet consensus standards.