Liquid metal embedded elastomers (LMEEs) have attracted interest from researchers on account of their combination of low elastic modulus, high flexibility, and tunable electrical and/or thermal conductivity. One interesting feature of LMEEs is that their electrical resistance remains constant when stretched, which is desirable in many real-world applications. This work aims to investigate this unique electromechanical coupling behavior of LMEEs with three-dimensional deterministic and statistical modeling. We first performed finite element analysis (FEA) of the electromechanical coupling response of a percolated liquid metal droplet repeating in the conductive network. Next, we modeled the internal conductive network of LMEE as a simple cubic structure and introduced stochasticity in representing the droplet–droplet connectivity. This combined approach allows us to calculate relative changes in resistance with stretch that are in reasonable agreement with experimental findings. Our analysis provides new theoretical insights that can guide efforts to tailor the electromechanical coupling behavior of LMEEs.

液态金属嵌入弹性体 (LMEE) 因其结合了低弹性模量、高柔韧性和可调节的导电性和/或导热性而引起了研究人员的兴趣。LMEE 的一个有趣特征是它们的电阻在拉伸时保持恒定，这在许多实际应用中是可取的。这项工作旨在通过三维确定性和统计建模来研究 LMEE 的这种独特的机电耦合行为。我们首先对在导电网络中重复的渗滤液态金属液滴的机电耦合响应进行了有限元分析 (FEA)。接下来，我们将 LMEE 的内部导电网络建模为简单的立方结构，并在表示液滴-液滴连通性时引入了随机性。这种组合方法使我们能够计算与实验结果合理一致的拉伸阻力的相对变化。我们的分析提供了新的理论见解，可以指导调整 LMEE 机电耦合行为的工作。