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<p>In this study, a novel analytical model has been developed for the auxetic three-dimensional (3D) star-shaped lattice structure, characterized by negative Poisson’s ratios and orthotropic symmetry. The developed analytical model, which fully incorporates geometric parameters such as reentrant angles and member length ratios, is capable of accurately predicting the effective mechanical properties. Compared to previous research, this work offers key advantages, including full 3D behavior modeling, closed-form solutions, and comprehensive evaluation of geometric interactions, while earlier studies were mostly limited to 2D models and numerical analysis. A predictive model is proposed based on Castigliano’s second theorem and Timoshenko beam theory to estimate the effective mechanical properties of 3D star-shaped lattice structures. The model accounts for axial, shear, and bending deformations, includes strut overlap in density calculations, and provides closed-form and implicit expressions for effective Young’s moduli, Poisson’s ratios, and compressive strength. The results are validated by finite element simulations in Abaqus and literature data. A parametric study reveals that re-entrant angles mainly influence Poisson’s ratios, while all geometric parameters affect stiffness and strength. The results show that with increasing auxetic properties, Young’s modulus and compressive (tensile) strength increase if some geometric parameters are adjusted properly. Potential applications of this work include energy-absorbing components in automotive systems, biomedical implants, light-weight aerospace structures, and smart mechanical systems. This research provides a foundation for designing multifunctional and tunable materials.</p>

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Mechanical behavior of a new orthotropic 3D star-shaped auxetic structure

  • 期刊论文

  • 发表日期：

    2026年4月18日

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  • Mohammad Noroozi,
  • Hamed Ahmadi,
  • Gholamhossein Liaghat,
  • Morteza Seidi

摘要

In this study, a novel analytical model has been developed for the auxetic three-dimensional (3D) star-shaped lattice structure, characterized by negative Poisson’s ratios and orthotropic symmetry. The developed analytical model, which fully incorporates geometric parameters such as reentrant angles and member length ratios, is capable of accurately predicting the effective mechanical properties. Compared to previous research, this work offers key advantages, including full 3D behavior modeling, closed-form solutions, and comprehensive evaluation of geometric interactions, while earlier studies were mostly limited to 2D models and numerical analysis. A predictive model is proposed based on Castigliano’s second theorem and Timoshenko beam theory to estimate the effective mechanical properties of 3D star-shaped lattice structures. The model accounts for axial, shear, and bending deformations, includes strut overlap in density calculations, and provides closed-form and implicit expressions for effective Young’s moduli, Poisson’s ratios, and compressive strength. The results are validated by finite element simulations in Abaqus and literature data. A parametric study reveals that re-entrant angles mainly influence Poisson’s ratios, while all geometric parameters affect stiffness and strength. The results show that with increasing auxetic properties, Young’s modulus and compressive (tensile) strength increase if some geometric parameters are adjusted properly. Potential applications of this work include energy-absorbing components in automotive systems, biomedical implants, light-weight aerospace structures, and smart mechanical systems. This research provides a foundation for designing multifunctional and tunable materials.