Effective temperature dynamics in an athermal amorphous plasticity theory

Recent developments in the theory of amorphous plasticity point to the central role played by the concept of an effective disorder temperature $T_{eff}$. An athermal dynamics for $T_{eff}$ is proposed in the framework of a deformation theory and discussed in light of recent steady-state simulations by Haxton and Liu [T. K. Haxton and A. J. Liu, Phys. Rev. Lett. 99, 195701 (2007)]. The structure of the resulting theory, its parameters and transient dynamics are discussed and compared to available data.

Figure 1

$T_{eff}^{\infty }$ vs ${\text{log}}_{10}\left({\tau }_0{D}^{tot}\right)$ in the simulations of Ref. [10]. Data courtesy of T. Haxton and A. Liu.

Figure 2

(Color online) $\overline{\mathcal{C}}$ as a function $s^{\infty }/s_y$ for $\beta =1$ (diamonds), $\beta =1.25$ (squares), and $\beta =1.5$ (circles).

Figure 3

(Color online) The deviatoric stress $s/s_y$ as a function of the imposed strain $\gamma \equiv {\int }_0^t{D}^{tot}\left(t^{\prime }\right)d{t}^{\prime }$. The arrows indicate the direction of the applied $D^{tot}$.

Figure 4

(Color online) The effective disorder temperature $T_{eff}$ as a function of the imposed strain $\gamma \equiv {\int }_0^t{D}^{tot}\left(t^{\prime }\right)d{t}^{\prime }$. The arrows indicate the direction of the applied $D^{tot}$.