### Atomistic Modeling at Experimental Strain Rates and Time Scales

X. Yan, P. Cao, W. Tao, P. Sharma and H.S. Park

Accepted for publication in *Journal of Physics D: Applied Physics* 2016 (invited topical review)

#### Abstract

Modeling physical phenomena with atomistic fidelity and at laboratory time-scales is one of the holy grails of computational materials
science. Conventional molecular dynamics (MD) simulations enable the elucidation of an astonishing array of phenomena inherent in the
mechanical and chemical behavior of materials. However conventional MD, with our current computational modalities, is incapable of
resolving time-scales longer than microseconds (at best). In this short perspective article, we briefly review a recently proposed
approach---the so-called autonomous basin climbing (ABC) method--- that in certain instances can provide valuable information on
slow-time-scale processes. We provide a general summary of the principles underlying the ABC approach, with emphasis on recent
methodological developments enabling the study of mechanically-driven processes at slow (experimental) strain rates and time scales.
Specifically, we show that by combining a strong physical understanding of the underlying phenomena, kinetic Monte Carlo, transition
state theory and minimum energy pathway methods, the ABC method has been found to be useful in a variety of mechanically-driven
problems ranging from prediction of creep-behavior in metals, constitutive laws for grain boundary sliding, void nucleation rates,
diffusion in amorphous materials to protein unfolding. Aside from reviewing the basic ideas underlying this approach, we emphasize
some of the key challenges encountered in our own personal research work and suggest future research avenues for exploration.

### Surface Shear Transformation Zones in Amorphous Solids

P. Cao, X. Lin and H.S. Park

*Physical Review E* 2014; 90:012311

#### Abstract

We perform a systematic study of the characteristics of shear transformation zones (STZs) that nucleate at free surfaces of two-dimensional
amorphous solids subject to tensile loading using two different atomistic simulation methods, the standard athermal, quasistatic (AQ) approach
and our recently developed self-learning metabasin escape (SLME) method to account for the finite temperature and strain-rate effects. In the
AQ, or strain-driven limit, the nonaffine displacement fields of surface STZs decay exponentially away from their centers at similar decay
rates as their bulk counterparts, though the direction of maximum nonaffine displacement is tilted away from the tensile axis due to surface
effects. Using the SLME method at room temperature and at the high strain rates that are seen in classical molecular dynamics simulations,
the characteristics for both bulk and surface STZs are found to be identical to those seen in the AQ simulations. However, using the SLME
method at room temperature and experimentally-relevant strain rates, we find a transition in the surface STZ characteristics where a loss
in the characteristic angular tensile-compression symmetry is observed. Finally, the thermally-activated surface STZs exhibit a slower
decay rate in the nonaffine displacement field than do strain-driven surface STZs, which is characterized by a larger drop in potential
energy resulting from STZ nucleation that is enabled by the relative compliance of the surface as compared to the bulk.
This paper is available in PDF form
.

### Strain-Rate and Temperature Dependence of Yield Stress of Amorphous Solids via Self-Learning Metabasin Escape Algorithm

P. Cao, X. Lin and H.S. Park

*Journal of the Mechanics and Physics of Solids* 2014; 68:239-250

#### Abstract

A general self-learning metabasin escape (SLME) algorithm (Cao et al., 2012) is coupled in this work with continuous shear
deformations to probe the yield stress as a function of strain rate and temperature for a binary Lennard-Jones (LJ) amorphous
solid. The approach is shown to match the classical molecular dynamics (MD) results at high strain rates where the MD results
are valid, but, importantly, is able to access experimental strain rates that are about ten orders of magnitude slower than
MD. In doing so, we find in agreement with previous experimental studies that a substantial decrease in yield stress is
observed with decreasing strain rate. At room temperature and laboratory strain rates, the activation volume associated
with yield is found to contain about 10 LJ particles, while the yield stress is as sensitive to a 1.5T_{g} increase
in temperature as it is to a one order of magnitude decrease in strain rate. Moreover, our SLME results suggest the SLME
and extrapolated results from MD simulations follow distinctly different energetic pathways during the applied shear
deformation at low temperatures and experimental strain rates, which implies that extrapolation of the governing deformation
mechanisms from MD strain rates to experimental may not be valid.
This paper is available in PDF form
.

### Strain-Rate and Temperature-Driven Transition in the Shear Transformation Zone for 2D Amorphous Solids

P. Cao, H.S. Park and X. Lin

*Physical Review E* 2013; 88:042404

#### Abstract

We couple the recently developed self-learning metabasin escape algorithm, which enables efficient exploration of the potential
energy surface (PES), with shear deformation to elucidate strain-rate and temperature effects on the shear transformation zone
(STZ) characteristics in two-dimensional amorphous solids. In doing so, we report a transition in the STZ characteristics that
can be obtained either through increasing the temperature, or decreasing the strain rate. The transition separates regions
having two distinct STZ characteristics. Specifically, at high temperatures and high strain rates, we show that the STZs have
characteristics identical to those that emerge from purely strain-driven, athermal quasistatic atomistic calculations. At
lower temperatures and experimentally-relevant strain rates, we use the newly coupled PES + shear deformation method to show
that the STZs have characteristics identical to those that emerge from a purely thermally activated state. The specific
changes in STZ characteristics that occur in moving from the strain-driven to thermally-activated STZ regime include a 33%
increase in STZ size, faster spatial decay of the displacement field, a change in deformation mechanism inside the STZ from
shear to tension, a reduction in the stress needed to nucleate the first STZ, and finally a notable loss in characteristic
quadrupolar symmetry of the surrounding elastic matrix that has previously been seen in athermal, quasistatic shear
studies of STZs.
This paper is available in PDF form
.

### Self-Learning Metabasin Escape Algorithm for Supercooled Liquids

P. Cao, M. Li, R.J. Heugle, H.S. Park and X. Lin

*Physical Review E* 2012; 86:016710

#### Abstract

A generic history-penalized metabasin escape algorithm that contains no predetermined parameters is presented in this work.
The spatial location and volume of imposed penalty functions in the configurational space are determined in self-learning processes
as the 3N-dimensional potential energy surface is sampled. The computational efficiency is demonstrated using a binary Lennard-Jones
liquid supercooled below the glass transition temperature, which shows an O(10^{3}) reduction in the quadratic scaling coefficient
of the overall computational cost as compared to the previous algorithm implementation. Furthermore, the metabasin correlation
lengths in these supercooled liquids are obtained as a natural consequence of determining the self-learned penalty function width
distributions. In the case of a bulk binary Lennard-Jones liquid at a fixed density of 1.2, typical metabasins are found to
contain about 148 particles while having a correlation length of 3.09 when the system temperature drops below the glass transition
temperature.
This paper is available in PDF form
.