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<p>This study presents an analytical investigation into the bending behavior of cylindrical Gyroid triply periodic minimal surface(TPMS) scaffolds, a critical factor for their success in load-bearing bone regeneration applications. By modeling the surrounding tissue as a Winkler-Pasternak elastic foundation and employing Higher-Order Shear Deformation Theory(HSDT), we derive and solve the governing equations to assess the scaffold’s mechanical performance. The primary objective is to establish definitive design principles for mitigating stress shielding by optimizing both the internal architecture and its interaction with the host environment. A systematic parametric analysis reveals that the spatial distribution of porosity profoundly impacts bending stiffness. Notably, a mid-plane peaked gradient design(PD I) significantly minimizes deflection—by concentrating solid material near the high-stress outer surfaces—outperforming uniform(PD III) and surface-porous(PD II) architectures. Furthermore, increased foundation stiffness dramatically enhances structural stability, while lower aspect ratios and higher relative densities improve rigidity, particularly in soft tissue environments. These findings provide essential, quantifiable guidelines for scaffold design. By tailoring the porosity gradient and geometric factors, it is possible to engineer implants that closely match the mechanical response of native bone, thereby effectively reducing the risk of stress shielding and promoting successful osseointegration. This work contributes a computationally efficient analytical framework that bridges the gap between complex numerical simulations and practical clinical design, offering a powerful tool for the development of patient-specific, functionally graded bone scaffolds.</p>

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Bending performance of functionally graded gyroid TPMS bone scaffolds on elastic foundations: an analytical approach for mitigating stress shielding

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • Sepide Nosrati,
  • Seyed Amirhosein Hosseini,
  • Omid Rahmani

摘要

This study presents an analytical investigation into the bending behavior of cylindrical Gyroid triply periodic minimal surface(TPMS) scaffolds, a critical factor for their success in load-bearing bone regeneration applications. By modeling the surrounding tissue as a Winkler-Pasternak elastic foundation and employing Higher-Order Shear Deformation Theory(HSDT), we derive and solve the governing equations to assess the scaffold’s mechanical performance. The primary objective is to establish definitive design principles for mitigating stress shielding by optimizing both the internal architecture and its interaction with the host environment. A systematic parametric analysis reveals that the spatial distribution of porosity profoundly impacts bending stiffness. Notably, a mid-plane peaked gradient design(PD I) significantly minimizes deflection—by concentrating solid material near the high-stress outer surfaces—outperforming uniform(PD III) and surface-porous(PD II) architectures. Furthermore, increased foundation stiffness dramatically enhances structural stability, while lower aspect ratios and higher relative densities improve rigidity, particularly in soft tissue environments. These findings provide essential, quantifiable guidelines for scaffold design. By tailoring the porosity gradient and geometric factors, it is possible to engineer implants that closely match the mechanical response of native bone, thereby effectively reducing the risk of stress shielding and promoting successful osseointegration. This work contributes a computationally efficient analytical framework that bridges the gap between complex numerical simulations and practical clinical design, offering a powerful tool for the development of patient-specific, functionally graded bone scaffolds.