Multi-material topology optimization of tunable multifunctional microstructures with nonlinear magnetic and thermal fields

초록

Multi-material microstructures provide a versatile means for tailoring multiple macroscopic properties beyond those of monolithic materials. Achieving reliable magnetic performance while ensuring efficient heat dissipation is essential for magnetic devices and motivates the concurrent design of magnetic and thermal responses. In this context, multifunctional material systems offer an expanded design space for meeting such combined requirements. However, most existing studies on magnetic fields remain limited to single-material systems. To address this limitation, a novel multi-material inverse homogenization framework is proposed to facilitate microstructure design by considering both magnetic and thermal fields. In this approach, micromechanics-based homogenization is employed to evaluate effective properties. A discrete-material-optimization-based interpolation scheme was adopted to represent the spatial distribution of two-phase ferromagnetic materials with inherent trade-offs between magnetic permeability and thermal conductivity and was further modified using exponential interpolation to improve numerical characteristics. To obtain balanced multifunctional designs, a global criterion method was introduced to integrate multiple physical performance criteria into a unified objective function. Several numerical examples were presented to demonstrate the effectiveness of the proposed framework. The results showed that multi-material designs under multi-field conditions offer apparent benefits over their single-material or single-field counterparts and that considering magnetic nonlinearity leads to distinct design outcomes. Furthermore, systematic performance tuning was achieved through material volume fraction control, and directional magnetic responses were realized by introducing an additional orthotropy constraint. This study provides insights into the engineering design of hybrid material systems, highlighting the potential of multi-material and multi-field approaches for achieving controllable and application-relevant functional performance.

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