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Homogenization-driven microstructure compatibility for multiscale topology optimization
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DOI：10.1016/j.cma.2026.118984.png)
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Abstract
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When microstructures are arranged periodically or gradiently to form multiscale architectures, ensuring their physical compatibility remains a fundamental yet challenging design requirement. Previous studies predominantly focus on analyzing specific configurations with limited physical-field generalizability or on enforcing geometric compatibility. In this paper, we propose a novel concept of physical compatibility, termed homogenization-driven microstructure compatibility, that rigorously quantifies the interfacial consistency between two microstructures with prescribed property tensors. The core of our framework lies in homogenization theory. We use it to encode the discrepancy between two responses. One is the physical response of a direct assembly of microstructures, treated as distinct geometric constructs. The other is the response of an assembly of their homogenized equivalents, regarded as effective continuum materials. Theoretically, this compatibility is applicable to various physical fields as long as the corresponding homogenization is available. In this work, we successfully apply this compatibility in mechanical and thermal multiscale topology optimization, achieving a remarkable reduction in the performance discrepancy between the multiscale design and full-scale structure after microstructure combination. Our compatibility is more general than the previous physical compatibility and enables a substantially larger design space than geometric compatibility approaches.
Keywords:
homogenization-driven compatibility
multiscale topology optimization
microstructure design
physical compatibility
homogenization theory
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7.3
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1.3W
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5.6W
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