Two-subsystem thermodynamics for the mechanics of aging amorphous solids

Abstract

The effect of physical aging on the mechanics of amorphous solids as well as mechanical rejuvenation is modeled with nonequilibrium thermodynamics, using the concept of two thermal subsystems, namely a kinetic one and a configurational one. Earlier work (Semkiv and Hütter in J Non-Equilib Thermodyn 41(2):79-88, 2016) is extended to account for a fully general coupling of the two thermal subsystems. This coupling gives rise to hypoelastic-type contributions in the expression for the Cauchy stress tensor, that reduces to the more common hyperelastic case for sufficiently long aging. The general model, particularly the reversible and irreversible couplings between the thermal subsystems, is compared in detail with models in the literature (Boyce et al.

Two-scale model for the effect of physical aging in elastomers filled with hard nanoparticles

“…The framework used in this paper to formulate the dynamics of the system is the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) [21][22][23], which has also been used in our preceding work [5,17,18]. It is a formal thermodynamic procedure to set up evolution equations for a set of variables X .…”

“…To describe the physical aging of the glassy bridges, one needs to be able to model the physical aging of the glassy matrix material. As discussed in detail in [17,18] and references therein, a practical way to achieve that is by accounting for an additional thermal variable. This is needed in order to mimic the fact that, in the glassy state, there is a substantial difference between the (rapid) relaxation and equilibration of vibrations around energy minima on the one hand, and on the other hand the population of different low-energy states by way of transitions across high energy barriers (by rare events).…”

“…This is needed in order to mimic the fact that, in the glassy state, there is a substantial difference between the (rapid) relaxation and equilibration of vibrations around energy minima on the one hand, and on the other hand the population of different low-energy states by way of transitions across high energy barriers (by rare events). This discrepancy in dynamics can be captured by splitting the total entropy of the glassy material into its so-called kinetic (s) and configurational (η) parts, where the former describes the local intra-basin dynamics in the energy landscape, while the latter describes the much slower inter-basin dynamics [17,18]. For the current study, however, one notices that only η needs to be included in the set of variables, while s can be obtained by subtracting η and the filler particle entropy from s t .…”

“…First, the physical aging and mechanical rejuvenation can be studied from a thermodynamic perspective for bulk glassy polymers, e.g. as done in [15][16][17][18]. Second, the lessons learned from that latter work can be built into the two-scale nanocomposite model developed in [5], which is the topic of this paper.…”

Modeling energy storage and structural evolution during finite viscoplastic deformation of glassy polymers

“…Enthalpy relaxation, and more broadly structural relaxation, has been explained successfully using the concept of a configurational temperature [21] or an equivalent order parameter [22,23] to describe the nonequilibrium ther- modynamic state of amorphous materials cooled below glass transition temperature [12,24]. The configurational temperature was first introduced as an internal variable called "the fictive temperature" by Tool [21], then as a thermodynamic property called "the effective temperature" in the two-temperature thermodynamic theory for amorphous materials [25][26][27][28]. The two-temperature theory assumes that the thermodynamic properties of an amorphous glass can be described by two weakly interacting material subsystems, an equilibrium kinetic subsystem that represents the fast vibrational motions and a nonequilibrium configurational subsystem that represents the slow configurational rearrangements of the polymer segments.…”