Topology optimization of multifunctional materials for property control under nonlinear magnetic and linear elastic fields

Abstract

This study presents a novel material design methodology for multifunctional microstructures that simultaneously considers nonlinear magnetic and linear elastic fields. While real-world magnetic applications require the combined analysis of multiple physical phenomena such as magnetic nonlinearity and mechanical performance, prior microscale design methods have rarely addressed magnetic saturation and have yet to integrate it with structural stiffness in a unified manner. This work fills that gap by realizing tunable behavior through coupled-field design at the microscale. The approach employed micromechanics-based homogenization, readily adaptable to multi-field regimes, to derive effective material properties within a finite element framework, and was further extended to capture material nonlinearity. An inverse homogenization technique was then developed to optimize the microstructures, enabling extreme performance and precise control over the targeted properties. Finally, the optimization process identified the structural layouts that balance superior mechanical responses with tailored nonlinear magnetic profiles, offering a new design strategy for magneto-mechanical material design. The process was validated using three numerical examples: (1) maximizing the magnetic response, (2) achieving the prescribed nonlinear permeabilities, and (3) demonstrating multifunctional capabilities. The results confirm the effectiveness of the proposed approach, showing improved nonlinear magnetic functionality across all saturation regions and controlled specific anisotropic magnetic behavior. Notably, the multifunctional design exhibited enhanced mechanical characteristics, showing an 8.73 % increase in the bulk modulus and a 45.48 % improvement in the shear modulus compared with considering only magnetic fields, while maintaining the desired magnetic performance. These findings highlight the potential of the current study for the lightweight, performance-driven architectural design of advanced electromagnetic devices.