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26 The PCB Magazine • June 2014 it is pinned to zero while the bottom disk guar- antees the surface strain to be zero across the complete surface area of the small disk [12] and suppresses any sharp peak strain across the non- deformable to deformable surface [15] . We compare the effects of embedding one disk and two disks by using a combination of finite element simulations and experimental measurements. Let us first consider embedding a single disk close to the surface of the substrate. Since the plastic disk is much stiffer than the elastomeric substrate, such a construct is highly non-sym- metric. When the substrate is stretched, the thin disk bends into a concave shape (Figure 2a). Far away from the disk, the substrate becomes flat. To make a transition from the concave shape above the disk to the flat shape far away from the disk, the substrate bends into a convex shape right off the edge of the disk. Consequently, the convex region of the substrate develops a large strain (Figure 2b). This high strain may cause failure of the interconnects [12] . To reduce the strain on the surface of the substrate, we embed a second, larger, disk, roughly at a depth about half of the thick- ness of the substrate. Because this large disk is placed in the mid-plane of the substrate, when the substrate is stretched, the two disks no longer bend significantly (Figure 2c). Con- sequently, the surface of the substrate above the edge of the bottom disk no longer devel- ops a high peak of strain (Figure 2d). Further- more, because the top disk is embedded close to the surface of the substrate, the strain on the surface of the substrate rapidly decays near the edge of the top disk, giving a large area for active devices. The strains determined from the finite element simulation agree well with experimental data. The strain in the two-disk HyBRID STRETCHABLE CIRCUITS oN SILICoNE SUBSTRATE continues Figure 2: surface strain profiles across the non-deformable to deformable interface when the substrate is stretched to 20% strain. (a) and (c) are the deformations of the finite element simulation in the case of a single disk and double disks embedded within the elastomer. the top disk is 100 lm from the sur- face and the bottom disk is half way through the substrate. the top and bottom disks are 5 mm and 8 mm in diameter, respectively. the scale in vertical direction is magnified 50%. (b) and (d) solid lines are the surface strain calculated from the finite element simulations. data points are the experimentally measured data.