STUDY ON THE MECHANICAL PROPERTIES OF SCHERK SINGLE-PERIODIC MINIMAL SURFACE

WANG Shuai; DENG Tao; HE Jialu; ZHOU Kaifa

doi:10.16579/j.issn.1001.9669.2025.08.006

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STUDY ON THE MECHANICAL PROPERTIES OF SCHERK SINGLE-PERIODIC MINIMAL SURFACE

·Experimental Research·Testing Technology· | 更新时间：2025-08-18

- STUDY ON THE MECHANICAL PROPERTIES OF SCHERK SINGLE-PERIODIC MINIMAL SURFACE
- Journal of Mechanical Strength Vol. 47, Issue 8, Pages: 48-58(2025)
- 作者机构：
  
  1.重庆工程职业技术学院智能制造与交通学院，重庆 402260
  2.重庆交通大学航空学院，重庆 400074
  3.重庆交通大学土木工程学院，重庆 400074
- 作者简介：
  
  WANG Shuai, E-mail：ws15993500427@163.com
- 基金信息：
  
  National Natural Science Foundation of China(52275051);Chongqing Jiaotong University Natural Science Unveiling Project(XJ2023000701);Chongqing Graduate Tutor Team Building Project(JDDSTD2022007);Chongqing Graduate Joint Training Base Construction Project(JDLHPYJD2022001)
- DOI：10.16579/j.issn.1001.9669.2025.08.006
  CLC： TG146.2
- Received：10 December 2023，
  
  Revised：16 January 2024，
  
  Published：15 August 2025
- 稿件说明：
移动端阅览
王帅，邓涛，何佳璐，等. Scherk单周期极小曲面力学特性研究［J］. 机械强度，2025，47（8）：48-58.

WANG Shuai，DENG Tao，HE Jialu，et al. Study on the mechanical properties of Scherk single-periodic minimal surface［J］. Journal of Mechanical Strength，2025，47（8）：48-58.
王帅，邓涛，何佳璐，等. Scherk单周期极小曲面力学特性研究［J］. 机械强度，2025，47（8）：48-58. DOI： 10.16579/j.issn.1001.9669.2025.08.006.

WANG Shuai，DENG Tao，HE Jialu，et al. Study on the mechanical properties of Scherk single-periodic minimal surface［J］. Journal of Mechanical Strength，2025，47（8）：48-58. DOI： 10.16579/j.issn.1001.9669.2025.08.006.

摘要

极小曲面具有空间连续光滑的特点，能够有效避免应力集中问题，成为力学超材料研究的重要关注方向。研究了一种Scherk单周期极小曲面（Single-Periodic Minimal Surface

SPMS），采用体素重构技术多软件联合生成了空间连续光滑几何模型。利用有限元仿真探究了单周期Scherk曲面结构的力学行为和能量吸收特性。分析了极小曲面数学参数对几何构型的影响规律，建立了五种不同参数的极小曲面，探求了在正压和侧压的条件下，五种结构的变形模式与应力分布。借助金属打印技术制作了Scherk曲面结构，并进行了准静态压缩试验。结果表明，Scherk单周期曲面具有明显的负泊松比效应，SPMS结构呈现的X形和V形变形模式，能够很好地承受外载荷作用。压缩试验表明，SPMS结构反力和位移曲线呈现驼峰现象，说明该结构表现出负泊松比和负刚度特性，该特性为其在几何大变形和能量吸收方面的应用研究提供了广阔的空间。

Abstract

Minimal surfaces are characterized by spatially continuous smoothness

which can effectively avoid the problem of the stress concentration

and have become a significant focus in the research of mechanical metamaterials. A Scherk single-periodic minimal surface (SPMS) was studied

and the spatially continuous smooth geometrical model was generated using a voxel reconstruction technique with multi-software association method. The mechanical behavior and energy absorption characteristics of the single-period Scherk surface structure were investigated using finite element simulation. The impact of the mathematical parameters of the minimal surface on the geometric configuration was examined. Five minimal surfaces with different parameters were established

and the deformation patterns and stress distributions of the five structures were explored under positive and lateral compression conditions. The Scherk surface structures were fabricated by metal printing technology

and quasi-static compression tests were conducted. The results show that the Scherk single-period surface has an obvious negative Poisson ratio effect

and the SPMS structure exhibits X-and V-shaped deformation modes

which can well withstand the external loading effects. The compression tests show the hump phenomenon of the reaction force and displacement curves of the SPMS structure

indicating that the structure has a negative Poisson ratio and negative stiffness property. This property provides a wide space for its application research in large deformation damage and structural energy absorption.

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