  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 non-linear elasticity on the mechanical and thermodynamic
properties of amorphous materials responding to shear, using effective field
and gravitational theories. The predicted correlations among the non-linear
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 towards understanding 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.
