Fabrication of the slipknot
All experiments were conducted at room temperature (21 °C). The loading rate was set at 10 mm min–1 during the slipknot-tying process. To ensure the reproducibility of the slipknots, we used a standardized fabrication method with a 3D-printed string-wrapping board. The designed grooves of the board conformed to the spatial configuration of the slipknot (Extended Data Fig. 1). String was wrapped along these grooves to produce standardized slipknots. The upper right side and lower right end of each slipknot were clamped, and the untightened slipknot was subjected to tension using a Zwick/Roell Z010 testing machine until a preset force F tying was achieved. Following this procedure, standardized slipknots with F tying were fabricated.
High-speed camera recordings
We used a high-speed camera (C321, Phantom) to capture the evolution of slipknot configurations during release from the front view (Fig. 2a(i–v)). The camera operated at 11,000 f.p.s. with a 10-μs electronic shutter speed using macro lenses (100MM F2.8 CA-Dreamer Macro ×2 lenses, Anhui Changgeng Optics Technology). It recorded images at 640 × 128 pixels with a 10-bit depth.
Micro-CT scanning
We used a micro-CT system (Xradia 610 Versa, Zeiss) with a voxel size of 1.3 × 1.3 × 1.3 µm3 to scan slipknots and to reconstruct their 3D structures based on five typical states. The micro-CT system was set to operate at 120 kV and 17.5 W. Each scan involved an exposure time of 2,500 ms per projection, during which the slipknots were securely positioned and examined for approximately 170 min. We fabricated an in situ tensile fixture (Supplementary Fig. 18) that fit in the sample chamber of the micro-CT scanner. This fixture enabled application of a preset tensile force to the slipknot, allowing it to be gradually opened to any desired state and maintaining it in a stable configuration throughout the scanning process. Micro-CT modelling and analyses were performed using Amira 3D software (v.2021.1, Thermo Fisher Scientific).
FEM of slipknots
FEM of the string slipknot was performed using Abaqus 2020 and the Abaqus/Explicit solver for computations. A model representing the slipknot was formulated using 8-node linear brick mesh elements with reduced integration and hourglass control (C3D8R). The material behaviour of the string was characterized by elastoplasticity. Elasticity was captured by using linear elasticity with an elastic modulus of 2,700 MPa and a Poisson’s ratio of 0.49. The plasticity was captured by using a plasticity model of combined hardening by fitting cyclic tensile test data (Supplementary Note 1 and Supplementary Fig. 19). The contact condition was modelled using a general contact-type interaction with a friction coefficient of 0.16 (Extended Data Fig. 6).
The simulation processes of slipknot tying, tightening and opening were visualized. First, the string was tied into a slipknot by implementing prescribed displacement sequences to the key points along the string. Second, the slipknot was tightened with a preset force. The pre-tension was maintained in one step and was unloaded afterwards. Third, the slipknot was opened by moving the free end away from the fixed end.
Mechanical test
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