Effective-medium theory of a filamentous triangular lattice

Area of Science:

• Materials Science
• Condensed Matter Physics
• Statistical Mechanics

Background:

• Filamentous networks are crucial in various scientific domains.
• Understanding their mechanical response is essential for predicting material behavior.
• Existing models often simplify the complex interplay of forces within these structures.

Purpose of the Study:

• To develop an effective-medium theory incorporating both bending and stretching forces.
• To analyze the mechanical response of a diluted filamentous triangular lattice.
• To identify critical thresholds and elastic regimes in these networks.

Main Methods:

• Formulated an effective-medium theory for filamentous lattices.
• Included central-force springs for bonds and bending forces between neighboring bonds.
• Investigated lattice behavior as a function of bond probability (p).

Main Results:

• Identified a rigidity threshold (p(b)) independent of bending rigidity.
• Observed a crossover between bending, stretching, and coupled elastic regimes.
• Characterized the influence of central-force rigidity percolation (p(CF) ≈ 2/3) when bending rigidity is negligible.

Conclusions:

• The developed theory accurately describes the mechanical response of diluted filamentous lattices.
• Bending forces play a critical role in determining the rigidity and elastic behavior of these networks.
• The study provides insights into the transition between different mechanical regimes in complex filamentary materials.