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Strain Localization in an Oscillating Maxwell Viscoelastic Cylinder
Panagiotis G Massouros1, Philip V Bayly2, Guy M Genin2
1Department of Mechanical Engineering and Materials Science Washington University in St. Louis.
International Journal of Solids and Structures
|May 31, 2014
Summary
Transient rotation responses in viscoelastic structures are key for magnetic resonance imaging. A Maxwell viscoelastic cylinder exhibits a surprising strain field singularity during wave propagation, impacting material characterization and brain mechanics.
Area of Science:
- Continuum Mechanics
- Biophysics
- Material Science
Background:
- Transient rotation responses of viscoelastic structures are crucial for interpreting experiments.
- Magnetic resonance techniques are used to characterize materials and closed structures like the brain.
- Understanding these responses aids in material characterization and understanding biological systems.
Purpose of the Study:
- To investigate the response of a Maxwell viscoelastic cylinder to outer boundary displacement.
- To analyze the development and behavior of the transient strain field.
- To explore the implications of observed phenomena for brain mechanics and morphology.
Main Methods:
- Mathematical modeling of a simple, axisymmetric, Maxwell viscoelastic cylinder.
- Application of small, sinusoidal displacement to the outer boundary.
- Closed-form calculation of the transient strain field using conventional approaches.
Main Results:
- A surprising strain field singularity develops as the wavefront propagates.
- The singularity appears at the center, reflects, and persists through multiple cycles.
- The singularity is repeatedly annihilated and reinitiated until steady-state oscillations are reached.
Conclusions:
- The study presents a closed-form solution for the transient strain field in a viscoelastic cylinder.
- A persistent singularity in the strain field was identified and characterized.
- This singularity may play a role in the mechanical response and morphological evolution of the brain.
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