Michael Shields1 Falk Michael1 Christopher Rycroft2 Dihui Ruan1 Darius Alix-Williams1

1, Johns Hopkins University, Baltimore, Maryland, United States
2, Harvard University, Cambridge, Massachusetts, United States

The shear transformation zone (STZ) theory provides a rigorous framework for continuum modeling of plastic deformation in amorphous solids. The STZ theory relies upon the notion of an effective disorder temperature defined by Teff=∂Uc/∂Sc, where Uc is the configurational energy and Sc the configurational entropy – making it a “structural” analog to the classical vibrational thermodynamic temperature. Over sufficiently large length-scales it is hypothesized that the density of STZs scales with the effective temperature (i.e. higher effective temperature implies higher density of STZs). The STZ theory further defines a flow rule such that plastic deformation at a given stress state scales with the STZ density. Hence, regions of the material with higher effective temperature are more susceptible to plastic rearrangement than regions with low effective temperature.

In this work, we explore the inherently stochastic nature of effective temperature fluctuations of metallic glasses. We start by quantifying random variations in potential energies at the atomistic scale and utilize an affine transformation [1] to coarse-grain to a continuum level random field description of the effective temperature [2]. Careful statistical investigation of the atomic potential energies and their coarse-grained fields may provide evidence for medium-to-long range correlations in the potential energies and a minimum coarse-graining length-scale when defining effective temperature initial conditions from atomistic simulations. The continuum STZ model is calibrated using a surrogate-based efficient global optimization (EGO) [3] routine and the sensitivity of the STZ model to coarse-graining parameters is investigated [4]. This serves to motivate the need for, at a minimum, stochastic modeling of continuum STZ equations based on random field effective temperature initial conditions. More generally though, this study coupled with some further observations suggest a roadmap toward a fully stochastic model of plastic deformation in amorphous metals that builds from the structural disorder at the atomistic level and enables statistically consistent continuum modeling at higher length-scales.

[1] Y. Shi, M. B. Katz, H. Li, and M. L. Falk, “Evaluation of the Disorder Temperature and Free-Volume Formalisms via Simulations of Shear Banding in Amorphous Solids,” Phys. Rev. Lett., vol. 98, no. 18, p. 185505, May 2007.
[2] A. R. Hinkle, C. H. Rycroft, M. D. Shields, and M. L. Falk, “Coarse graining atomistic simulations of plastically deforming amorphous solids,” Phys. Rev. E, vol. 95, no. 5, 2017.
[3] D. R. Jones, M. Schonlau, and W. J. Welch, “Efficient Global Optimization of Expensive Black-Box Functions,” J. Glob. Optim., vol. 13, no. 4, pp. 455–492, 1998.
[4] D. Giovanis and M. D. Shields, (In Review) “Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations,” J. Comput. Phys.