The equivalent medium of cellular substrate under large stretching, with applications to stretchable electronics

The concepts of open, cellular substrates for stretchable electronic systems are of interest partly due to their ability to minimize disruptions to the natural diffusive or convective flow of bio-fluids in advanced, bio-integrated implants. The overall elastic properties, and in particular the stretchability, of such systems are difficult to determine, however, because they depend strongly on the alignment and position of the serpentine interconnects relative to the openings in the cellular substrate, which is difficult to precisely control, even with the assistance of precision stages and visualization hardware. This paper establishes an analytic constitutive model for an equivalent medium for a cellular substrate under finite deformation. Results demonstrate that the elastic stretchability of a serpentine interconnect bonded to this equivalent medium represents a lower-bound estimate for the case of the actual cellular substrate, where the bonding adopts different alignments and positions. This finding provides a simple, conservative estimate of stretchability, which has general utility as an engineering design rule for platforms that exploit cellular substrates in stretchable electronics.