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<p>This paper proposed a topology optimization method for nearly incompressible hyperelastic materials using three-field mixed finite element formulation. The Mooney-Rivlin model is used to describe the constitutive relations of hyperelastic materials. The volume locking problem caused by nearly incompressibility is solved using three-field mixed finite element formulation. The topology optimization model under finite deformation assumptions aims to minimize the structural end-compliance with volume constraint. The energy interpolation scheme is employed for circumventing numerical convergence issues caused by low-density elements. The adjoint method is used to obtain the sensitivity information. Numerical examples verify the effectiveness of the proposed method. The magnitude of load and bulk modulus for the structure significantly affects the results of topology optimization. Finally, the complete 299-line MATLAB code and detailed explanations are provided to learn and use for junior researchers.</p>

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299-line topology optimization code of nearly incompressible hyperelastic materials using three-field mixed finite element

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Huiqiang Guo,
  • Xinyu Xie,
  • Fei Cheng,
  • Zhengguang Li,
  • Ran Zhang,
  • Jiantao Bai,
  • Wenjie Zuo

摘要

This paper proposed a topology optimization method for nearly incompressible hyperelastic materials using three-field mixed finite element formulation. The Mooney-Rivlin model is used to describe the constitutive relations of hyperelastic materials. The volume locking problem caused by nearly incompressibility is solved using three-field mixed finite element formulation. The topology optimization model under finite deformation assumptions aims to minimize the structural end-compliance with volume constraint. The energy interpolation scheme is employed for circumventing numerical convergence issues caused by low-density elements. The adjoint method is used to obtain the sensitivity information. Numerical examples verify the effectiveness of the proposed method. The magnitude of load and bulk modulus for the structure significantly affects the results of topology optimization. Finally, the complete 299-line MATLAB code and detailed explanations are provided to learn and use for junior researchers.