Mean-field homogenization of liquid metal elastomer composites: comparative study and exact dilute solution of core–shell inclusion

Liquid metal-elastomer composites (LMECs) have gathered significant attention for their potential applications in various functional stretchable devices, with inclusion sizes ranging from micrometers to nanometers. These composites exhibit exceptional properties, such as high electric permittivity and thermal conductivity, surpassing those of the elastomer matrix, thus enabling a broader range of applications without compromising the material's stretchability. To investigate the diverse effective elastic and functional properties of LMECs, micromechanics-based homogenization method based on Eshelby's inclusion solution are invaluable. However, the extreme contrast in elastic constants among the phases in LMECs, particularly for nanosized inclusions where a considerable amount of stiff metal oxide forms around the inclusions, can lead to critical failure in predicting effective properties if inadequate homogenization approach is employed. In this study, we present multiple mean-field homogenization approaches applicable to LMECs with core-shell morphology, namely: (i) multi-phase, (ii) sequential, (iii) pseudo-grain, and (iv) direct approaches. We compare the accuracy of the models concerning effective elastic, thermal, and dielectric properties, evaluated against numerical homogenization results and compared with reported experimental data. Specifically, we highlight homogenization scheme utilizing exact field solutions of dilute core-shell inclusion, emphasizing the importance of accurately capturing the field in the micromechanics of LMECs. Furthermore, we demonstrate that widely utilized interphase model could not properly resolve the core-shell morphology and thus should be avoided. This comprehensive assessment provides critical insights into the proper homogenization strategies for designing advanced LMECs with precise prediction of effective properties.