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Interlocking-induced stiffness in stochastically microcracked materials beyond the transport percolation threshold
R C Picu1, A Pal1, M V Lupulescu2
1Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
Physical Review. E
|May 14, 2016
Summary
Stochastically microcracked materials maintain stiffness above the transport percolation threshold due to interlocking. Nonlinear mechanical behavior arises from fractal fragmentation, not crack roughness.
Area of Science:
- Continuum mechanics
- Materials science
- Percolation theory
Background:
- Microcracked continua exhibit complex mechanical behaviors.
- Percolation thresholds define critical transitions in material properties.
- Understanding stiffness and nonlinearity in fractured materials is crucial.
Purpose of the Study:
- Investigate the mechanical behavior of 2D microcracked continua.
- Analyze material stiffness and nonlinearity near percolation thresholds.
- Determine the influence of crack density and fractal fragmentation.
Main Methods:
- Numerical simulations of stochastically microcracked continua.
- Analysis of mechanical response across varying crack densities.
- Focus on crack densities near and above the transport percolation threshold.
Main Results:
- Materials retain stiffness significantly above the transport percolation threshold.
- Topological interlocking of subdomains preserves stiffness.
- Nonlinear mechanical behavior emerges between transport and stiffness percolation thresholds.
- Fractal fragmentation, not crack roughness, drives nonlinearity.
Conclusions:
- Topological interlocking is key to stiffness retention in microcracked materials.
- Fractal fragmentation introduces nonlinearity even with linear constitutive laws.
- The study provides insights into the mechanical response of fractured media.
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