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Micro and Macroscopic Stress-Strain Relations in Disordered Tessellated Networks
Ran Li1, Seyedsajad Moazzeni1, Liping Liu1,2
1Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854, USA.
Physical Review Letters
|May 19, 2023
Summary
Microscopic stress and strain in rigid, incompressible networks follow a simple relationship (σ=pE) due to energy minimization. This finding simplifies predictions for the shear modulus (μ=⟨p⟩/2) in randomized lattices.
Area of Science:
- Physics
- Materials Science
- Mechanics of Materials
Background:
- Understanding the mechanical behavior of complex networks like foams and tissues is crucial.
- Previous models often lack a simple, universal relationship between microscopic stress and strain.
Purpose of the Study:
- To establish a fundamental relationship between microscopic stress and strain in rigid, incompressible networks.
- To derive a simplified prediction for the shear modulus of such networks.
Main Methods:
- Analysis of mechanical equilibrium in rigid, incompressible networks.
- Application of energy minimization principles.
- Derivation of stress-strain relationships based on network properties.
Main Results:
- A simple linear relationship, σ=pE, was demonstrated between deviatoric stress (σ) and mean-field strain (E), governed by hydrostatic pressure (p).
- Microscopic stress and strain were found to align along principal directions, with predominantly affine deformations.
- The derived relationship is independent of specific energy models (e.g., foam, tissue).
Conclusions:
- The study reveals a universal stress-strain relationship in equilibrium networks, simplifying mechanical analysis.
- A direct prediction for the shear modulus (μ=⟨p⟩/2) was established for randomized lattices.
- The findings offer insights into the mechanical response of diverse network materials.
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