Modeling electromechanical behaviors of soft conductive composites embedded with liquid metal fibers

Soft conductive materials are key components of soft electronics, sensors, actuators, and wearable devices. The electrical conductivity matrix or tensor of soft conductive materials is usually deformation-dependent, but there is a lack of constitutive modeling work on it. To fill this knowledge gap, we consider a soft conductive composite embedded with liquid metal fibers as an example. The difference between the material conductivity and spatial conductivity is clarified briefly. In addition, we devise two constitutive models for the deformation-dependent conductivity tensors. These two models are equivalent but in different formats, one using stretch ratios and the other using invariants. Besides the conductivity models, a transversely isotropic hyperelastic model is also presented to model the mechanical behaviors. These analytical models are fitted and validated using data from multiphysics computational modeling on representative volume elements. Note that the proposed models can also be used for other soft conductive materials as well as thermal conductivity modeling.