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<p>4D printing is an advanced manufacturing technology that combines three-dimensional printing with the temporal dimension, enabling two-dimensional prefabricated parts to self-fold into three-dimensional structures. However, existing studies have mainly focused on the self-folding behavior of simple geometries. This study proposes a rapid parameter design and high-precision self-folding method for complex models. The complex structures consist of self-folding units and feature surfaces, with each self-folding unit composed of a composite of shape memory polymer and thermoplastic polyurethane. Through simulations and experiments, the bending factors of the self-folding units were comprehensively analyzed. Moreover, multi-factor experiments revealed the effects of different factor combinations on bending behavior and established a fitting model (R² = 0.92 and 0.90), enabling efficient determination of crease design parameters. Based on this, the self-folding workflow for complex models was optimized, and a crease filling interference optimization algorithm was proposed, reducing the crease optimization time by approximately 85%. Experimental results show that complex self-folding structures using the fitting model and optimization algorithm achieved an average deformation accuracy of 93%. This study provides theoretical guidance and practical strategies for the application of 4D printing in deployable structures and adaptive soft robotics.</p>

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Rapid design of self-folding parameters and performance for complex models based on 4D printing

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Rui Zhou,
  • Yunteng Jiang,
  • Chunzhi Du,
  • Hao Wu,
  • Xingjie Zhang

摘要

4D printing is an advanced manufacturing technology that combines three-dimensional printing with the temporal dimension, enabling two-dimensional prefabricated parts to self-fold into three-dimensional structures. However, existing studies have mainly focused on the self-folding behavior of simple geometries. This study proposes a rapid parameter design and high-precision self-folding method for complex models. The complex structures consist of self-folding units and feature surfaces, with each self-folding unit composed of a composite of shape memory polymer and thermoplastic polyurethane. Through simulations and experiments, the bending factors of the self-folding units were comprehensively analyzed. Moreover, multi-factor experiments revealed the effects of different factor combinations on bending behavior and established a fitting model (R² = 0.92 and 0.90), enabling efficient determination of crease design parameters. Based on this, the self-folding workflow for complex models was optimized, and a crease filling interference optimization algorithm was proposed, reducing the crease optimization time by approximately 85%. Experimental results show that complex self-folding structures using the fitting model and optimization algorithm achieved an average deformation accuracy of 93%. This study provides theoretical guidance and practical strategies for the application of 4D printing in deployable structures and adaptive soft robotics.