ITR-free undetectable heat-flux concentrator designed by density-based topology optimization

This study presents a density-based topology optimization framework for designing interfacial-thermal-resistance-free (ITR-free) undetectable heat-flux concentrators. Conventional thermal metamaterials typically rely on multi-material composites, where internal interfaces introduce ITR that inevitably degrades performance, especially at micro- and nanoscales. To overcome this fundamental limitation, we extend the ITR-free concept to multifunctional devices by representing spatially varying effective thermal conductivity through the thickness modulation of a single material. A topology optimization scheme is formulated based on a two-dimensional equivalent heat conduction model under the thin-domain approximation, in which the local structural height is treated as the design variable. This enables the simultaneous realization of thermal cloaking and heat-flux concentration within a single-material system. Two competing objective functions — evaluating the reproduction accuracy of the undisturbed external field and the amplification of heat flux within the target region — are integrated using the satisficing trade-off method (STM). Adjoint sensitivities are derived, and the density field is updated using the method of moving asymptotes (MMA) with minor modifications. Numerical demonstrations confirm that the optimized single-material structures successfully achieve both strong heat-flux focusing and minimal external detectability. Parametric studies further examine the influences of penalty exponents, volume constraints, maximum allowable thickness, and the thermal conductivity of the inner sensing region. The results demonstrate the potential of the proposed framework for designing ITR-free thermal devices within the thin-domain approximation.