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<p>Mechanical metamaterials with engineered coefficients of thermal expansion (CTEs) hold promising potential for a broad range of advanced applications. Although previous studies have demonstrated metamaterials with large positive, near-zero, or negative CTEs, the thermal expansion behavior of such structures typically lacks continuous tunability. To address this limitation, this paper proposes a topology optimization approach for designing the cell structure configuration of multiphase metamaterials with graded interfaces, enabling a broad and continuously tunable range of CTEs. The extended two-step filtering method is applied to model multiphase cell structures and explicitly control the width of interfaces between different solid phases. The SIMP-based interpolation scheme is employed to define the constitutive material phases and their interfaces, capturing both monotonic and non-monotonic gradient transitions. Additionally, the numerical homogenization technique is integrated with the SIMP approach to compute the effective properties of the metamaterials, supporting the inverse design process. Finally, a topology optimization formulation is developed to determine the configuration of cell structures that can achieve the desired CTE tuning by changing the width of interfaces. Numerical results demonstrate the effectiveness of this approach in generating optimized multiphase mechanical metamaterials with targeted and tunable CTE performance.</p>

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Topological Optimization Design of Multiphase Mechanical Metamaterials with Tunable Thermal Expansion Considering Graded Interface

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Yu Wang,
  • Qingyao Mo,
  • Kaibin Yao,
  • Shan Zeng,
  • Chao Jiang,
  • Bo Tang,
  • Xinghui Deng

摘要

Mechanical metamaterials with engineered coefficients of thermal expansion (CTEs) hold promising potential for a broad range of advanced applications. Although previous studies have demonstrated metamaterials with large positive, near-zero, or negative CTEs, the thermal expansion behavior of such structures typically lacks continuous tunability. To address this limitation, this paper proposes a topology optimization approach for designing the cell structure configuration of multiphase metamaterials with graded interfaces, enabling a broad and continuously tunable range of CTEs. The extended two-step filtering method is applied to model multiphase cell structures and explicitly control the width of interfaces between different solid phases. The SIMP-based interpolation scheme is employed to define the constitutive material phases and their interfaces, capturing both monotonic and non-monotonic gradient transitions. Additionally, the numerical homogenization technique is integrated with the SIMP approach to compute the effective properties of the metamaterials, supporting the inverse design process. Finally, a topology optimization formulation is developed to determine the configuration of cell structures that can achieve the desired CTE tuning by changing the width of interfaces. Numerical results demonstrate the effectiveness of this approach in generating optimized multiphase mechanical metamaterials with targeted and tunable CTE performance.