Non-linear elasticity, yielding and entropy in amorphous solids

Abstract

The holographic principle has proven successful in linking seemingly unrelated problems in physics; a famous example is the gauge-gravity duality 1 . Recently, intriguing correspondences between the physics of soft matter and gravity are emerging 2, 3 , including strong similarities between the rheology of amorphous solids, effective field theories for elasticity and the physics of black holes 4-7 . 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.

Shear flows in far-from-equilibrium strongly coupled fluids

“…[70][71][72]). Finally, our results provide another case in favor of "the unreasonable effectiveness of hydrodynamics" [73,74] and might have a physical impact not only on the out-of-equilibrium dynamics in heavy-ion collisions and QGP [20,23,75,76] but also on the understanding and characterization of rheological response of complex fluids [63,67,77] using the holographic tool [78].…”

“…Finally, let us emphasize that one could equivalently introduce a non-trivial strain into the dual field theory using the profile of the scalars ψ I . In particular, a shear strain could be simply obtained by allowing for a background of the type ψ 1 ∼ y as done in [77,84,85]. For practical reasons, we found more convenient to introduce the strain via a metric deformation.…”

Holographic Supersolids

“…Before proceeding to the results of our work, let us briefly describe how the holographic model at hand naturally includes mechanical deformations. Our notations follow closely the ones adopted in the EFT framework of [82,83]. Importantly, we will assume the deformations to be finite, or even large, and we will therefore consider the full framework of nonlinear elasticity.…”

Thermoelectric Transport in Holographic Quantum Matter under Shear Strain

“…Nevertheless, nonlinear elastic response can be obtained using holographic methods, yielding a rich phenomenology of nonlinear elasticity behaviours, see e.g. [22][23][24][25]. Given the full stress-strain curves, one can define the nonlinear elastic shear modulus G ≡ dΣ/dε.…”

“…In holography, the non-linear mechanical response was first introduced in [21] where the nonlinear stressstrain curves as well as an estimate of the elasticity bounds in the elastic regime were discussed. More recently, based on the effective field theory and holographic duality, a potential relationship among the nonlinear elasticity, yielding and entropy of granular matter was suggested and then verified by computer simulations of granular models [22]. The thermodynamic and mechanical properties of a holographic bottom-up model for the supersolid were considered in [23].…”