From bendable to stretchable
A thin ribbon bends easily but tears if you try to stretch it: metals fracture at a percent or two of tensile strain, yet skin and dura routinely deform by tens of percent. Conformal electrodes on cortex, an epidermal patch on skin, or a cuff on a moving nerve all demand true stretchability — the ability to survive large area strain without cracking the conductors.
The dominant trick is to hand the strain to geometry rather than to the material. A stretchable interconnect is routed as a serpentine or 'horseshoe' rather than a straight line: when the substrate stretches, the meander unwinds by bending out of plane, so the local material strain in the metal stays far below the global strain applied to the sheet.
Buckling, turned into a feature
A second, elegant strategy is controlled buckling. Bond a stiff thin film to a pre-stretched elastomer, then release the pre-strain: the film cannot compress, so it wrinkles into a regular sinusoid. The wavelength is set by the competition between film bending and substrate deformation.
Wrinkle wavelength of a stiff film (thickness t, plane-strain modulus Ē_f) on a soft substrate (Ē_s). The wrinkles let the film stretch by flattening.
Now the film can accommodate applied stretch simply by flattening its wrinkles — no material strain, no cracks — up to roughly the pre-strain you built in. Serpentine routing and pre-strain buckling are the two workhorses of stretchable electronics, and they are routinely combined.
Conformal contact — cortex, dura, and skin
Soft enough, and an array will cling to a wet, folded surface by van der Waals adhesion alone, following every sulcus and gyrus. This is the physics behind the conformal ECoG array — a thin, high-density sheet that hugs the cortical surface far more intimately than a rigid grid — and the electronic dura mater (e-dura), a soft implant designed to replace a patch of dura and ride the spinal cord's motion for years.
The materials palette makes this possible. An elastomer substrate (PDMS) gives the soft, stretchable backbone; a conductive hydrogel can be tuned to the kilopascal modulus of tissue itself and even bond adhesively to it; and mixed ionic–electronic conductors like PEDOT:PSS or the organic electrochemical transistor (OECT) use volumetric capacitance to move charge across the soft interface with low impedance. On skin, the same ideas yield the epidermal 'tattoo' electrode — a sub-micron film that laminates onto the epidermis and moves with it.