Non-Fourier heat conduction in 2D thermal metamaterials

The challenge of achieving precise control over heat conduction has persisted for years. Recent advancements in thermal metamaterials have offered a promising avenue for addressing this challenge. Yet, predicting the behaviors of non-Fourier heat conduction within these metamaterials remains elusive. In this study, we leveraged the extended plane wave expansion method (EPWEM) to decipher the complex band structures inherent to twodimensional (2D) thermal metamaterials. To ascertain the reliability of our approach, wave transmission in the time-domain and band structures derived from the finite element method (FEM) were juxtaposed against EPWEM results. Our findings revealed the presence of both directional and complete band-gaps in the complex band structures. Then a thermal bridge is predicted via the proposed complex band structure strategy and demonstrated numerically. By shedding light on non-Fourier heat conduction within thermal metamaterials, our analysis paves the way for groundbreaking applications in domains like laser hardening, laser cladding, metal additive manufacturing, and so on.