Indentation of adhesive beams

An exact dual-integral formulation of the indentation of finite, free-standing, end-supported adhesive elastic layers

“…This approach fails when the layer’s thickness is such that contact deformations are accommodated locally and not in the layer’s global deformation. Indeed, the inset in Figure 12(a) shows that the vertical displacements of the layer’s top and bottom surfaces are consistently lower when we follow the approximate approach [26]. This translates into the layer displaying higher stiffness.…”

“…For brevity of presentation, we will restrict ourselves to clamped and simply supported adhesive elastic layers. We have shown elsewhere in the context of contact of elastic beams [26] that these two boundary conditions bound the range of behaviours displayed by layers held between flexible end supports.…”

“…Punati et al [26] experimentally investigated the indentation of a clamped PDMS (poly-dimethyl-siloxane) layer by a cylindrical glass punch. To make PDMS samples, a uniform mixture of Sylgard 184 silicone elastomer base and curing agent is prepared by taking them in 10:1 weight ratio.…”

“…Finally, we compare our results for adhesive, free-standing layers with those due to more approximate approaches [26]. We consider several geometric and material parameters for the layers and plot variation of the total load P with punch displacement δ in Figure 12.…”

“…From Figure 12(a), we observe that with decreasing l ∕ h approximate theories are erroneous. This is because Punati et al [26] estimated the vertical displacement of the layer’s bottom surface by replacing the distributed interaction pressure on the layer’s top surface by a point load. This approach fails when the layer’s thickness is such that contact deformations are accommodated locally and not in the layer’s global deformation.…”