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<p>Mechanical metamaterials have garnered significant scientific attention due to their non-conventional and tailorable mechanical properties, which are dictated by their microstructural topologies. This work introduces a novel approach for designing periodic cellular materials with extreme mechanical properties, specifically aiming to maximize effective properties, e.g., bulk or shear moduli, under a prescribed volume fraction constraint. The proposed approach integrates Asymptotic Homogenization (AH) theory into the Sequential Element Rejection and Admission (SERA) topology optimization method, resulting in the AH-SERA framework. The homogenization results are then coupled with the SERA sensitivity analysis in a joint flowchart to govern the selective rejection or admission of elements within the design domain. Numerical 2D and 3D examples demonstrate that the proposed methodology generates diverse optimal topologies for the same objective function, achieved by tuning various parameter configurations of the SERA method. Furthermore, AH-SERA is compared against other reported literature methods, demonstrating its competitiveness by achieving objective function values comparable to or exceeding those reported in prior works.</p>

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Topological design of mechanical metamaterials based on homogenization theory and Sequential Element Rejection And Admission topology optimization method

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Mariela Gómez-Castañeda,
  • Arturo Gómez-Ortega,
  • Juan Manuel Alvarado-Orozco

摘要

Mechanical metamaterials have garnered significant scientific attention due to their non-conventional and tailorable mechanical properties, which are dictated by their microstructural topologies. This work introduces a novel approach for designing periodic cellular materials with extreme mechanical properties, specifically aiming to maximize effective properties, e.g., bulk or shear moduli, under a prescribed volume fraction constraint. The proposed approach integrates Asymptotic Homogenization (AH) theory into the Sequential Element Rejection and Admission (SERA) topology optimization method, resulting in the AH-SERA framework. The homogenization results are then coupled with the SERA sensitivity analysis in a joint flowchart to govern the selective rejection or admission of elements within the design domain. Numerical 2D and 3D examples demonstrate that the proposed methodology generates diverse optimal topologies for the same objective function, achieved by tuning various parameter configurations of the SERA method. Furthermore, AH-SERA is compared against other reported literature methods, demonstrating its competitiveness by achieving objective function values comparable to or exceeding those reported in prior works.