Analytical approximation of the two-dimensional percolation threshold for fields of overlapping ellipses

Area of Science:

• Materials Science
• Physics
• Computational Modeling

Background:

• Percolation theory is vital for understanding material properties influenced by microstructures.
• Existing models often simplify particle shapes, lacking applicability to variable aspect-ratio ellipses.
• No analytical approximation exists for generalized elliptical particle percolation.

Purpose of the Study:

• To develop and validate an analytical approach for determining percolation points in two-phase materials with elliptical particles.
• To investigate the impact of particle aspect ratio on percolation thresholds.
• To provide a foundation for extending the model to three-dimensional ellipsoidal particles.

Main Methods:

• Derivation of an analytical percolation model for elliptical particles.
• Verification of the analytical model using computational simulations.
• Analysis of cluster sizes and percolation status in elliptical and circular particle networks.

Main Results:

• An analytical percolation approach for generalized ellipses was successfully derived and validated.
• The study quantifies the relationship between particle aspect ratio and the percolation threshold.
• Simulations confirmed the model's accuracy in networks of elliptical and circular particles.

Conclusions:

• The developed analytical method accurately predicts percolation in materials with elliptical particles.
• Particle aspect ratio significantly influences the percolation threshold, offering design insights.
• This work lays the groundwork for understanding percolation in complex biological and engineered materials.