Stretchable electronics represents a relatively recent class of technology [1,2] of interest partly due to its potential for applications in sensory robotic skins, [3,4] conformal photovoltaic modules, [5,6] wearable communication devices, [7,8] skin-mounted monitors of physiological health, [9][10][11] advanced, soft surgical and clinical diagnostic tools, [11,12] and bioinspired digital cameras. [13,14] A key challenge in each of these systems is in the development of strategies in mechanics that simultaneously allow large levels of elastic stretchability and high areal coverages of active devices built with materials that are themselves not stretchable (e.g., conventional metals) and are, in some cases, highly brittle (e.g., inorganic semiconductors). For design approaches that embed stretchability in interconnect structures that join rigid device islands, the system level stretchability ε system is much smaller than the interconnect stretchability ε interconnect . Zhang et al. [15] identified the following relationship between the interconnect and system stretchability:, where f dev = (area of active device components)/(total area of the system) is the areal coverage ratio of active device components. Structure designs for stretchable interconnects have evolved from straight [13,16] to curvilinear interconnects, [17] from those bonded to or embedded in the supporting substrate [11,18] to free-standing designs housed in microfluidic enclosures, [19] and from simple structures [17] to fractal/self-similar designs. [15,[20][21][22] All such cases, including a broad variety of shapes, sizes, and geometric arrangements, share the same underlying mechanisms, i.e., out-of-plane buckling of thin structures (metals, insulators, or semiconductors with thickness typically between ≈100 nm and ≈1 µm) provides the basis for elastic stretchability. The most advanced interconnects achieve elastic (reversible)
