A mathematical model for predicting the electro-mechanical behavior of crack-based flexible strain sensor

Abstract

Crack-based flexible strain sensor generally shows significantly high sensitivity due to crack propagation induced conductive path reduction during stretching. To quantitatively analyze the relationship among strain, crack density, and device sensitivity, an electro-mechanical mathematical model is developed for investigating the performance of a carbon nanotube-silicon oxide/polydimethylsiloxane (CNT-SiOx/PDMS) based crack strain sensor. Strength and energy criteria are used to predict the crack density for SiOx/PDMS under different strains. The results are utilized with the probability distribution based cellular automata method to determine the crack distribution for further electrical analysis, which is related to the conductive and non-conductive classification of elements. Finally, the potential distribution for whole elements is calculated, leading to the investigation of sensitivity toward the CNT-SiOx/PDMS based strain sensor. The maximum predicted crack density of the SiOx/PDMS can reach 41.36 × 10−3 μm−1 under 60% tensile strain with a deviation of 5.23% compared to the experimental data. Correspondingly, the maximum predicted sensitivity of the device can reach 512.81 at a SiOx thickness of 3.93 μm, with the deviation of 9.25%. Based on the predicted results, it can be concluded that crack density affects the distribution and quantity of conductive elements. When stress is applied to the device, the crack density increases, and the conductive elements located in the crack area undergo a disconnection process, resulting a significant reduction in the conductive path and a rapid increase in sensitivity for strain sensor.