Nonlinear elasticity, yielding, and entropy in amorphous solids.

The holographic duality has proven successful in linking seemingly unrelated problems in physics. Recently, intriguing correspondences between the physics of soft matter and gravity are emerging, including strong similarities between the rheology of amorphous solids, effective field theories for elasticity, and the physics of black holes. However, direct comparisons between theoretical predictions and experimental/simulation observations remain limited. Here, we study the effects of nonlinear elasticity on the mechanical and thermodynamic properties of amorphous materials responding to shear, using effective field and gravitational theories. The predicted correlations among the nonlinear elastic exponent, the yielding strain/stress, and the entropy change due to shear are supported qualitatively by simulations of granular matter models. Our approach opens a path toward understanding the complex mechanical responses of amorphous solids, such as mixed effects of shear softening and shear hardening, and offers the possibility to study the rheology of solid states and black holes in a unified framework.