What is it about?
Estimating the fields induced by physical inhomogeneities has been central to physics and materials science for over 150 years, with foundational work by Maxwell, Rayleigh, and Einstein. Here, we solved this long-standing challenge by deriving the first 3D universal exact solution in Fourier space via a generalized equivalent inclusion method. This solution, previously considered unattainable, yield exact expressions for the effective physical moduli of magnetoelectroelastic composites and a general expression for the stress intensity factors of arbitrarily shaped cracks, enabling accurate predictions of macroscale properties and guiding the design of advanced materials. Our solutions are validated through comparisons with classical solutions and applied to diverse problems, including auxetic material design, strain engineering in battery anodes, and quantum dot optimization.
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Why is it important?
We unify single and multiple inhomogeneities under a universal framework, enabling exact predictions of effective properties in magnetoelectroelastic composites and rendering approximation-based methods obsolete. This advance enables transformative applications—from auxetic material design to magnetoelectric optimization—and lays a foundation for cross-disciplinary research and engineering across length scales.
Perspectives
I learned a lot in writting this cross-disciplinary paper. It is a pleasant process to perform this study since my collaborators are nice, efficient, and knowledgable!
Jiaming Zhu
Shandong University
Read the Original
This page is a summary of: Universal exact solutions for multiphysical inhomogeneities and inclusions in Fourier space, Proceedings of the National Academy of Sciences, October 2025, Proceedings of the National Academy of Sciences,
DOI: 10.1073/pnas.2508181122.
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