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Updated: May 12, 2025
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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
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Straight Disclinations in Fractional Nonlocal Medium.
Tamara Kyrylych1, Yuriy Povstenko1
1Department of Mathematics and Computer Science, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland.
Materials (Basel, Switzerland)
|May 7, 2025
Summary
This study introduces a new nonlocal elasticity theory using a fractional diffusion Green function kernel. It successfully models stress fields around disclinations without singularities, advancing continuum mechanics.
Area of Science:
- Continuum Mechanics
- Nonlocal Elasticity Theory
- Mathematical Physics
Background:
- Classical elasticity theory faces challenges with material behavior at small scales.
- Nonlocal stress tensors are crucial for capturing size effects and singularities.
- Integral formulations are essential for nonlocal constitutive relations.
Purpose of the Study:
- To develop a novel nonlocal elasticity theory.
- To model stress fields around straight wedge and twist disclinations.
- To eliminate nonphysical singularities in stress fields.
Main Methods:
- Utilizing a Green function of the fractional diffusion equation as the nonlocality kernel.
- Applying Laplace integral transform with respect to the nonlocality parameter.
- Analyzing solutions for disclinations in an infinite medium.
Main Results:
- Derived stress fields for straight wedge and twist disclinations.
- Demonstrated the transition from nonlocal to local behavior as the nonlocality parameter approaches zero.
- Confirmed the absence of nonphysical singularities at disclination lines.
Conclusions:
- The proposed nonlocal elasticity theory effectively models disclination stress fields.
- The use of a fractional diffusion Green function kernel provides a physically meaningful approach.
- This framework offers a singularity-free description of stress concentrations.
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