Configuration-Induced Directional Nonlinearity Enhancement in Composite Thermal Media

Abstract

Nonlinear thermal response enables flexible heat manipulation and management with artificial structures. In particular, intrinsic temperature-dependent parameters of constitutive materials guide the design of self-adaptive thermal metamaterials. However, the geometrical effect in nonlinear composites has not been adequately studied, which may limit the potential multiple functionalities and versatile control. Here, under the effective medium approximation framework, we develop a unified theory for predicting anisotropic nonlinear equivalent thermal conductivities of elliptical inclusions in homogeneous media. By means of the derived results, enhancement of value in nonlinear coefficient can be achieved in a specified direction, based on geometrically anisotropic configurations and temperature-dependent properties. Quantitative relations between directional enhancement and inclusive shape factors are given by analytical theory and verified by numerical simulation. The proposed theoretical methods can be further extended to arbitrary non-circular configurations of complex structures, and the directional nonlinearity enhancement effect will facilitate refined heat control, combined with other nonlinear mechanisms such as spatiotemporal modulation or harmonic generation.