Effective Permittivity and Permeability of Triply Periodic Minimal Surface Structures

This communication investigates a simple and efficient approach for evaluating the effective permittivity of triply periodic minimal surface (TPMS) structures. In the proposed approach, each unit cell of the TPMS is first uniformly divided into many thin layers along the parallel and vertical directions of the incident electric field, forming the parallel and the series two models. Each layer can be homogenized as a diagonal anisotropic medium using the Bruggeman (BM) effective medium theory. Then the transversal and the longitudinal entries of the effective permittivity tensors for a unit cell are obtained using the parallel and the series equivalent formula, respectively. Finally, the calculated permittivity tensor entries are averaged to further equivalent the TPMS structure as a uniform isotropic medium. Numerical examples are presented to study and validate the effectiveness of the proposed approach.