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Normal Stresses, Contraction, and Stiffening in Sheared Elastic Networks
Karsten Baumgarten1, Brian P Tighe1
1Delft University of Technology, Process & Energy Laboratory, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands.
Physical Review Letters
|April 26, 2018
Summary
Stretching elastic solids causes a nonlinear Poynting effect, leading to normal stresses. This study links the Poynting effect to the Grüneisen parameter, revealing how vibrations in networks predict material stiffening under shear.
Area of Science:
- Solid mechanics
- Materials science
- Statistical physics
Background:
- The Poynting effect describes nonlinear normal stresses in sheared elastic solids.
- The Grüneisen parameter relates material deformation to changes in vibrational properties.
Purpose of the Study:
- To establish a novel relationship between the Poynting effect and the microscopic Grüneisen parameter.
- To apply this relationship to random spring networks, modeling materials like gels and foams.
- To investigate the predictive power of the Poynting effect for material stiffening.
Main Methods:
- Theoretical analysis connecting the Poynting effect and Grüneisen parameter.
- Modeling of random spring networks as a minimal elastic solid.
- Simulation and analysis of network behavior under shear deformation.
Main Results:
- A new quantitative relation between the Poynting effect and the Grüneisen parameter was derived.
- Random spring networks were found to contract or develop tension upon stretching due to increased vibrational frequency.
- The amplitude of the Poynting effect was shown to depend on the network's elastic moduli and connectivity.
Conclusions:
- The Poynting effect in elastic solids is fundamentally linked to microscopic vibrational changes quantified by the Grüneisen parameter.
- This link provides a mechanism for volume changes and tension development in network materials upon stretching.
- The Poynting effect serves as a predictor for the onset of shear-induced stiffening in materials at finite strains.
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