Mode-mixity-dependent adhesion of power-law graded elastic solids under normal load and substrate stretch-induced mismatch strain

The present paper analytically investigates the adhesive behavior of power-law graded elastic solids under a combined action of external normal loading and a substrate stretch-induced mismatch strain with the effect of mode-mixity taken into account. A plane strain non-slipping model, a plane strain non-coupling model and an axisymmetric non-coupling model have been analyzed, respectively. Our results show that under a finite normal force, the equilibrium of the adhesive system may lost its stability at a critical value of mismatch strain, which significantly depends on both the graded material constants and the degree of mode-mixity. This indicates that the strongest or weakest adhesion strength under substrate stretching can be achieved by designing the physical constants of the adhesive system appropriately. These results provide a theoretical foundation for novel applications of functional graded materials in adhesion systems.