Two-subsystem thermodynamics for the mechanics of aging amorphous solids

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. in Mech Mater 7:15-33, 1988; Buckley et al. in J Mech Phys Solids 52:2355-2377, 2004; Klompen et al. in Macromolecules 38:6997-7008, 2005; Kamrin and Bouchbinder in J Mech Phys Solids 73:269-288, 2014; Xiao and Nguyen in J Mech Phys Solids 82:62-81, 2015). It is found that only for the case of Kamrin and Bouchbinder (J Mech Phys Solids 73:269-288, 2014) there is a nontrivial coupling between the thermal subsystems in the reversible dynamics, for which the Jacobi identity is automatically satisfied. Moreover, in their work as well as in Boyce et al. (Mech Mater 7:15-33, 1988), viscoplastic deformation is driven by the deviatoric part of the Cauchy stress tensor, while for Buckley et al. (J Mech Phys Solids 52:2355-2377, 2004) and Xiao and Nguyen (J Mech Phys Solids 82:62-81, 2015) this is not the case