Nonaffine displacements and the nonlinear response of a strained amorphous solid

Abstract

We demonstrate that irreversible structural reorganization is not necessary for the observation of yield behavior in an amorphous solid. While the majority of solids strained to their yield point do indeed undergo an irreversible reorganization, we find that a significant fraction of solids exhibits yield via a reversible strain. We also demonstrate that large instantaneous strains in excess of the yield stress can result in complete stress relaxation, a result of the large nonaffine motions driven by the applied strain. The empirical similarity of the dependence of the ratio of stress over strain on the nonaffine mean-square displacement to that for the shear modulus obtained from quiescent liquid at nonzero temperature supports the proposition that rigidity depends on the size of the sampled configurational space only and is insensitive to how this space is sampled.

Rejuvenation and shear banding in model amorphous solids

“…with i and j coordinate components. Since local strains are not affine in general (particularly in glasses [44]) the previous formula will no longer be exact for each individual atom-neighbor pair. For two configurations separated by a small macroscopic strain interval, as proposed by Zimmerman et al [45], we define the atomic-level deformation tensor F α ij for atom α by minimizing the function…”

“…with i and j coordinate components. Since local strains are not affine in general (particularly in glasses [44]) the previous formula will no longer be exact for each individual atom-neighbor pair.…”

Precursors of fluidisation in the creep response of a soft glass

“…This rigid phase, however, does not correspond to an equilibrium state in the thermodynamic limit where the free energy of any phase of a system cannot depend on the shape of its boundary 11,12 . Thus, solids that sustain a finite stress are in a nonequilibrium state and, provided that one waits long enough, they would eventually evolve into a stress-free state under the application of even an infinitesimal stress [13][14][15][16][17] . The time associated with the approach of the latter equilibrium state may in general exceed any observable scales and, in this sense, rigid or yield-stress materials are very long-lived metastable systems.…”

Yielding of a model glass former: An interpretation with an effective system of icosahedra

“…However it is understood that glasses under simple shear undergo particle displacements in two different regimes; below a certain threshold, the system lies in the transient regime where (mostly) reversible, elastic deformations take place. Beyond this threshold, the system undergoes irreversible, plastic deformations to a large extent [8]. The threshold between these two regimes is the yield point [3,4].…”