Thermalized formulation of soft glassy rheology

Abstract

We present a version of soft glassy rheology that includes thermalized strain degrees of freedom. It fully specifies systems' strain-history-dependent positions on their energy landscapes and therefore allows for quantitative analysis of their heterogeneous yielding dynamics and nonequilibrium deformation thermodynamics. As a demonstration of the method, we illustrate the very different characteristics of fully-thermal and nearly-athermal plasticity by comparing results for thermalized and nonthermalized plastic flow.

Thermalization of plastic flow versus stationarity of thermomechanical equilibrium in SGR theory

“…1 (and in Ref. [32]) needs to be challenged. Nevertheless, there are many reasons to believe a thermalized SGR theory -and ideally, a partially/variably thermalized SGR theory -is desirable, and we should not give up the effort to develop one.…”

“…Nevertheless, there are many reasons to believe a thermalized SGR theory -and ideally, a partially/variably thermalized SGR theory -is desirable, and we should not give up the effort to develop one. Prominent among these reasons is the desire to extend the applicability of SGR theory from the nearly-athermal materials it was originally designed to treat to more-thermal amorphous materials such as metallic, small-molecule, and polymeric glasses [32,31]. These materials' postyield response depends very strongly on T , e.g.…”

“…This choice of α is motivated by recent soft-spot studies [5,6,7] suggesting α 2 ≃ 10 for metallic glasses; values for polymeric glasses should be similar [36]. The value of each macroscopic physical quantity ζ(ǫ) is given by [21,32]…”

“…This means that when zones yield, their configurations (u, ǫ el ) are reset to new configurations (u ′ , ǫ el ′ ) that are minimally stable [have E(u, ǫ el ) < 0] but otherwise are selected randomly. In contrast, thermalized SGR [31,32] assumes that the new configurations are fully equilibrated by systems' fast degrees of freedom. Specifically, it assumes that fully-thermalized plastic flow is obtained when f (u, ǫ el , T ) = w eq (u, ǫ el , T )Θ(δ − |ǫ el |), where w eq (u, ǫ el , T ) is (u, ǫ el )-zones' equilibrium statistical weight.…”

“…As in Ref. [32], we employ an idealized, highly aged initial condition wherein systems have reached thermomechanical equilibrium [w(u, ǫ el ) t=0 = w eq (u, ǫ el , T )] and then numerically integrate Eq. 1 forward in time for various f (u, ǫ el , T ).…”