Normal stresses, contraction, and stiffening in sheared elastic networks

Abstract

When elastic solids are sheared, a nonlinear effect named after Poynting gives rise to normal stresses or changes in volume. We provide a novel relation between the Poynting effect and the microscopic Grüneisen parameter, which quantifies how stretching shifts vibrational modes. By applying this relation to random spring networks, a minimal model for, e.g., biopolymer gels and solid foams, we find that networks contract or develop tension because they vibrate faster when stretched. The amplitude of the Poynting effect is sensitive to the network's linear elastic moduli, which can be tuned via its preparation protocol and connectivity. Finally, we show that the Poynting effect can be used to predict the finite strain scale where the material stiffens under shear.

5 pages, 5 figures

References in corpus (12)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Elasticity of Stiff Polymer Networks
• Auxetic metamaterials from disordered networks
• Nonaffine rubber elasticity for stiff polymer networks
• Non-affine response: jammed packings versus spring networks
• Soft Sphere Packings at Finite Pressure but Unstable to Shear
• Jamming in finite systems: stability, anisotropy, fluctuations and scaling
• Crosslinked networks of stiff filaments exhibit negative normal stress
• Softening and Yielding of Soft Glassy Materials
• Floppiness, cutting, and freezing: Dynamic critical scaling near isostaticity
• Nonlocal elasticity near jamming
• Nonlinear elastic stress response in granular packings

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• Canceling the elastic Poynting effect with geometry
• Role of normal stress in the creep dynamics and failure of a biopolymer gel