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When elastic solids are sheared, a nonlinear effect named after Poyntinggives rise to normal stresses or changes in volume. We provide a novel relationbetween the Poynting effect and the microscopic Gr\"uneisen parameter, whichquantifies how stretching shifts vibrational modes. By applying this relationto random spring networks, a minimal model for, e.g., biopolymer gels and solidfoams, we find that networks contract or develop tension because they vibratefaster when stretched. The amplitude of the Poynting effect is sensitive to thenetwork's linear elastic moduli, which can be tuned via its preparationprotocol and connectivity. Finally, we show that the Poynting effect can beused to predict the finite strain scale where the material stiffens undershear.

Normal stresses, contraction, and stiffening in sheared elastic networks