Effect of temperature difference on the mechanical responses of ribbon kirigami: Toward the highly stretchable conductors

Abstract

Kirigami-patterned designs through photolithography technology present a promising set of strategy for highly stretchable conductors, which have been investigated to open up a wide range of novel technological solutions for various applications, such as stretchable bioprobe and wearable thermotherapy. The kirigami-patterned conductors usually suffer steady temperature difference and consequent thermal load, because of the Joule heating effect under input voltages. The concealed relationships between thermal effects, geometric effects and mechanical responses are of great significance for practical applications. Here, a closed-form analytical solution, considering the thermal effect and large curvature curved beam theory, is developed to study the stretchability and stiffness for a class of ribbon kirigami structures. Both of finite element method and experiments are performed to validate the accuracy and scalability of model. Comparisons of the developed closed-form stretchability and stiffness to the model with thermal effect absent present quantitative characteristic towards the thermal effect, the remarkable underestimate of stretchability (e.g., >8% relatively) and overestimate of stiffness (e.g., >5% relatively) can be induced by the thermal-effect-absent model for many representative ribbon kirigami patterns. Moreover, several demonstrations present the capability of developed model in optimization of ribbon-kirigami-patterned conductors under the thermal effect and practical geometry constraint conditions, achieving the most stretchable devices. This study provides the theoretical guide for kirigami-based conductor designs in applications.