Two-temperature continuum thermomechanics of deforming amorphous solids

Abstract

There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent, finite-deformation, continuum framework for deforming amorphous solids. The basic premise is that the configurational degrees of freedom of the material --- the part of the internal energy/entropy that corresponds to mechanically stable microscopic configurations --- are characterized by a configurational temperature that might differ from that of the vibrational degrees of freedom, which equilibrate rapidly with an external heat bath. This results in an approximate internal energy decomposition into weakly interacting configurational and vibrational subsystems, which exchange energy following a Fourier-like law, leading to a thermomechanical framework permitting two well-defined temperatures. In this framework, internal variables that carry information about the state of the material equilibrate with the configurational subsystem, are explicitly associated with energy and entropy of their own, and couple to a viscoplastic flow rule. The coefficients that determine the rate of flow of entropy and heat between different internal systems are proposed to explicitly depend on the rate of irreversible deformation. As an application of this framework, we discuss two constitutive models for the response of glassy materials, a simple phenomenological model and a model related to the concept of Shear-Transformation-Zones as the basis for internal variables. The models account for several salient features of glassy deformation phenomenology. Directions for future investigation are briefly discussed.Comment: 31 pages, 3 figure

Two-subsystem thermodynamics for the mechanics of aging amorphous solids

“…However, in order to account for the effect of physical aging, also called structural relaxation, a split of that thermal degree of freedom into its kinetic and configurational contributions is considered, in analogy to [12,14,15,20,23]. While from a practical (interpretation) point of view, one might be tempted to use two temperatures instead of two (partial) entropies, this would result in unnecessary technical complications, which would rather disguise the essence of the two-subsystem approach.…”

“…which have also been used frequently in the literature for modeling the two-subsystem thermodynamics [9][10][11][12][13][14][15]19]. From a macroscopic perspective, the two temperatures defined in (15) and (16) denote the variables conjugate to the respective subsystem entropies, which can be used to transition from the internal energy density as a thermodynamic potential to the Helmholtz free energy density, by Legendre transformation.…”

“…The formal description of aging dynamics often is based on a concept of internal state variables [3], particularly in the form of configurational temperature, first proposed by Tool [9], and then used intensively, e.g., in [10][11][12][13][14][15][16]. According to this concept, the amorphous solid is described by two, rather than one, thermal degrees of freedom, namely a kinetic one and a configurational one.…”

“…While the kinetic (vibrational) degree of freedom accounts for intra-basin thermodynamics, the configurational one describes the inter-basin thermodynamics [17][18][19][20][21][22][23][24]. Models have been developed for the evolution of the kinetic and configurational thermal degrees of freedom [10][11][12][13][14][15], as well as constitutive expressions have been formulated for a stress tensor and for a plastic flow rule for the mechanical deformation of aging solids. However, in these models the mutual interaction of the kinetic and configurational subsystems is in general incomplete, as discussed in the sequel of this paper, and leaves room for further investigation and generalization.…”

“…3), specifically including the nontrivial reversible coupling between the kinetic and configurational degrees of freedom. This general model is then compared in detail with other approaches in the literature, i.e., [3,6,10,14,15] (Sect. 4), before drawing conclusions (Sect.…”