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Shear stresses in fluid and solid membranes with bending elasticity.
1Bucknell University, Department of Mathematics, 1 Dent Drive, Lewisburg, Pennsylvania 17837, USA.
Physical Review. E
|August 1, 2025
Summary
Simple membrane models reveal how bending energy generates shear stresses via curvature and surface stress coupling. This occurs incidentally, regardless of whether the membrane is fluid or solid, impacting tangential flow resistance.
Area of Science:
- Materials Science
- Physics
- Biophysics
Background:
- Membrane mechanics often involves bending energy, but its relation to shear stress generation is complex.
- Understanding membrane behavior requires distinguishing between fluid and solid states and their stress responses.
Purpose of the Study:
- To investigate how bending energy in simple fluid and solid membrane models generates shear stresses.
- To differentiate the mechanical responses of fluid and solid membranes under tangential stress and flow.
Main Methods:
- Comparative analysis of fluid (Helfrich) and solid (Seung-Nelson) membrane bending energy models.
- Examination of the stress tensor's tangential components and their implications for membrane behavior.
Main Results:
- Fluidlike Helfrich bending energy inherently contributes shear stresses.
- Solidlike Seung-Nelson energy yields an isotropic tangential stress tensor.
- A distinction is made between resistance to tangential flow and the capacity to support tangential stress.
Conclusions:
- Shear stress generation in membranes is linked to bending energy and curvature-stress coupling, irrespective of material state.
- The findings clarify pseudomomentum balance and provide insights into membrane tether dynamics.
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