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Stiffness Percolation in Stochastically Fragmented Continua.
1Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
Physical Review Letters
|September 28, 2017
Summary
We discovered a fragmented material state that maintains stiffness through interlocking fragments. This state exhibits nonlinear mechanical behavior controlled by fragment contacts, revealing a stiffness percolation threshold.
Area of Science:
- Solid Mechanics
- Materials Science
- Continuum Mechanics
Background:
- Microcracked materials exhibit complex mechanical behaviors.
- Understanding material fragmentation is crucial for predicting structural integrity.
- Percolation theory provides a framework for studying connectivity in disordered systems.
Purpose of the Study:
- To investigate the mechanical behavior of 3D randomly microcracked continua.
- To identify the conditions and limits of a fully fragmented material state.
- To characterize the effective material stiffness across varying crack densities.
Main Methods:
- Simulating three-dimensional, randomly microcracked continua.
- Analyzing material response at crack densities up to and beyond the transport percolation threshold.
- Identifying the stiffness percolation threshold and quantifying stiffness variations.
Main Results:
- Demonstrated a fully fragmented material state with preserved stiffness due to topological interlocking.
- Observed nonlinear mechanical behavior governed by fragment contact mechanics in this regime.
- Quantified the stiffness percolation threshold as the upper limit for this behavior.
- Reported the variation of effective material stiffness from zero to the stiffness percolation threshold.
Conclusions:
- Topological interlocking enables stiffness preservation in highly fragmented materials.
- Fragment contact mechanics dictates nonlinear behavior in the fragmented regime.
- The stiffness percolation threshold marks a critical transition in the mechanical response of microcracked continua.
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