Layered half-space modeling of piezoelectric TPMS-based CNT/PDMS composites under surface loadings

The present study investigates the static response of homogenized piezoelectric (PE) composites comprising a carbon nanotube (CNT)-doped polydimethylsiloxane (PDMS) matrix reinforced with piezoelectrically active material distributed within a Primitive Triply Periodic Minimal Surface (TPMS) geometry, subjected to electric and mechanical loadings. The solution of each layer is expressed in terms of a cylindrical system of vector functions. The eigenvalue-eigenvector approach is utilized to obtain the layer solutions, while the Dual Variable and Position (DVP) method is employed to handle multilayered configurations efficiently. The results in the high-frequency physical domain are then obtained by applying appropriate boundary and interface conditions. For numerical investigations, CNT-doped PDMS matrices reinforced with a TPMS-based PE phase corresponding to the Primitive geometry are considered. In the absence of any agglomeration, the CNT volume fraction (VF) is set as 0.0%, 0.061%, and 0.602%, and the composites are referred to as NoAg-VF0, NoAg-VF0.061, and NoAg-VF0.602. On the other hand, two different levels of agglomeration, represented as ζ = 0.15 and 0.40, are considered. The CNT VFs at ζ = 0.15 are 0.07 and 0.693, while at ζ = 0.40, the CNT VFs are set as 0.09% and 0.891%. The composites so formed are referred to as Ag-VF0.07, Ag-VF0.693, Ag-VF0.09, and Ag-VF0.891. The TPMS-based PE phase is incorporated at VFs of 10%, 20%, 30%, and 40%. The results highlight the importance of microstructural optimization in designing advanced PE composites, with potential applications in geophysical sensors and large-scale devices.