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.

用于可拉伸电子系统的开放式蜂窝基板的概念引起人们的兴趣，部分原因是它们能够最大限度地减少对先进生物集成植入物中生物流体自然扩散或对流流动的干扰。然而，此类系统的整体弹性特性，特别是拉伸性，很难确定，因为它们强烈依赖于蛇形互连件相对于蜂窝基底中的开口的对准和位置，而这很难精确控制，即使在精密平台和可视化硬件的帮助下也是如此。本文建立了有限变形下蜂窝基底等效介质的解析本构模型。结果表明，接合到该等效介质的蛇形互连件的弹性拉伸性代表了实际蜂窝基板情况的下限估计，其中接合采用不同的对准和位置。这一发现提供了对可拉伸性的简单、保守的估计，对于在可拉伸电子产品中利用蜂窝基板的平台来说，它具有通用的工程设计规则。