Related Experiment Video
Updated: Jul 19, 2025
11:41
Magnetic Tweezers for the Measurement of Twist and Torque
Published on: May 19, 2014
23.3K
Torsion and bistability of double-twist elastomers
Matthew P Leighton1, Laurent Kreplak2, Andrew D Rutenberg2
1Department of Physics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada.
Soft Matter
|August 14, 2023
Summary
Anisotropic elastomers exhibit a Poynting-like effect, coupling twist and extension. Structural bistability occurs at low strains, undergoing a bifurcation under specific boundary conditions, crucial for understanding collagen fibril mechanics.
Area of Science:
- Materials Science
- Solid Mechanics
- Biophysics
Background:
- Anisotropic elastomers with double-twist director fields model biological structures like collagen fibrils and blue phases.
- Understanding their elastic properties is key to predicting material behavior under mechanical stress.
Purpose of the Study:
- To investigate the elastic properties of anisotropic elastomers with a double-twist director field.
- To analyze the Poynting-like effect and structural bistability under varying boundary conditions.
Main Methods:
- Theoretical modeling of anisotropic elastomers with a double-twist director field.
- Analysis of the coupling between torsion and extension.
- Examination of structural bistability and bifurcations under different boundary conditions (freely-rotating vs. clamped).
Main Results:
- A significant Poynting-like effect was observed, demonstrating a coupling between torsion and extension.
- Structural bistability was identified at very small extensional strains for freely-rotating boundary conditions.
- A saddle-node bifurcation occurred at approximately 1% strain for collagen fibril parameters, absent under clamped conditions.
Conclusions:
- The study reveals a critical strain-induced structural transition in anisotropic elastomers.
- Boundary conditions significantly influence the observed mechanical behavior, particularly the presence of bifurcations.
- Residual torques are expected to induce helical shape effects when torsion is fixed, highlighting the importance of boundary constraints in experimental setups.
Related Concept Videos
01:13Angle of Twist - Elastic Range
357
Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
357
01:10Residual Stresses in Circular Shafts
195
In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the...
195
01:13Angle of Twist: Problem Solving
349
An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the...
349
01:16Torsion of Noncircular Members
159
Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
159
01:19Members Made of Elastoplastic Material
121
The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
As the bending moment...
121
01:20Bending and Torsional Moments
3.9K
Bending and torsional moments are two fundamental concepts in structural engineering. They play an important role in understanding the behavior of materials and structures under different loading conditions.
The reaction developed in a structural element when subjected to an external force causes the element to bend. When a structural element bends upwards, it creates compressive normal forces on the top and tensile normal forces on the bottom, resulting in a couple that determines the bending...
The reaction developed in a structural element when subjected to an external force causes the element to bend. When a structural element bends upwards, it creates compressive normal forces on the top and tensile normal forces on the bottom, resulting in a couple that determines the bending...
3.9K