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Published on: November 27, 2012
Dynamic buckling of morphoelastic filaments
Raymond E Goldstein1, Alain Goriely
1Department of Physics, University of Arizona, Tucson, Arizona 85721, USA.
Summary
Biological structures like filaments can change shape under stress over time. This study models morphoelasticity, showing how stress rate affects filament shape and allowing new equilibrium configurations.
Area of Science:
- Biophysics
- Mechanobiology
- Materials Science
Background:
- Biological structures exhibit equilibrium shapes influenced by external stresses.
- Morphoelasticity describes the interplay between material properties and shape changes.
- Filaments, such as bacterial filaments and plant tendrils, are common biological structures exhibiting complex shapes.
Purpose of the Study:
- To investigate the simplest model of morphoelasticity in filaments.
- To explore the effects of dynamic Euler buckling and writhing on filament shapes.
- To understand how externally imposed stresses, applied over time, alter equilibrium shapes.
Main Methods:
- Modeling a filament whose intrinsic curvatures relax to local curvatures.
- Analyzing dynamic Euler buckling and writhing phenomena.
- Simulating time-dependent stress application (ramping thrust or twist).
Main Results:
- The effective elastic properties of filaments are dependent on the load rate.
- Slowly applied stresses, even if removed, can result in a continuum of buckled shapes.
- Morphoelastic relaxation allows filaments to bypass traditional bifurcation points.
Conclusions:
- Filament shape is not solely determined by instantaneous stress but also by the history of applied stress.
- Dynamic stress application and relaxation offer new pathways for shape determination in biological filaments.
- This model provides insights into the adaptability and resilience of biological structures under mechanical load.
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