Applied Mathematics and Mechanics (English Edition) ›› 2026, Vol. 47 ›› Issue (9): 1901-1918.doi: https://doi.org/10.1007/s10483-026-3430-8

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A compression-torsion combined loading method for soft materials based on metamaterials

Ziji YIN, Lingling HU, Yongrou ZHANG()   

  1. School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, Guangdong Province, China
  • Received:2026-01-17 Revised:2026-06-25 Published:2026-09-17
  • Contact: Yongrou ZHANG, E-mail: zhangyr67@mail.sysu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (No. 12472400) and the Shenzhen Science and Technology Program of China (No. JCYJ20241202130001002)

Abstract:

Soft materials often experience complex multi-axial stress states in practical applications; however, most existing mechanical experimental studies are primarily limited to single-loading mode tests, owing to the technical and cost constraints of combined loading systems. In this paper, we propose a combined loading method for soft materials using a mechanically designed metamaterial. The inherent architecture of the metamaterial converts an input compressive load into a combined compressive-torsional output, enabling combined loading experiments with only a conventional universal testing machine. To match the low stiffness of soft materials, the metamaterial is fabricated from thermoplastic polyurethane and integrated with a metal plate at the specimen contact surface, ensuring visible torsional deformation under low pressure while retaining sufficient load-bearing capacity. Furthermore, when soft materials undergo large deformation, direct surface speckling for digital image correlation (DIC) becomes impractical due to the speckle distortion. To overcome this, a “brim” is incorporated to track the relative displacement between the metamaterial and loading platen, thereby allowing indirect calculation of the overall specimen strain. To ensure efficient torque transmission, the two end faces of the specimen need to be securely bonded. A correction method is also developed to mitigate the stress measurement errors caused by end-face bonding effects. Using silicone as a representative soft material, we validate the proposed approach by characterizing its mechanical response under combined compression-torsion loading and establishing a corresponding viscoelastic constitutive model. The results reveal notable strain-rate dependence and strong nonlinearity in the mechanical behavior of silicone, and suggest that constitutive parameters calibrated solely from uniaxial compression tests may be inadequate for predicting the behavior under complex stress states. The developed experimental technique provides an effective means for advancing the comprehensive mechanical characterization of soft materials under multi-axial loading.

Key words: combined compression-torsion loading, soft material, compression-torsion metamaterial

2010 MSC Number: 

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