Molecular dynamics simulations are performed to investigate the plastic response of a model glass to a local shear transformation in a quiescent system. The deformation of the material is induced by a spherical inclusion that is gradually strained into an ellipsoid of the same volume and then reverted back into the sphere. We show that the number of cage-breaking events increases with increasing strain amplitude of the shear transformation. The results of numerical simulations indicate that the density of cage jumps is larger in the cases of weak damping or slow shear transformation. Remarkably, we also found that, for a given strain amplitude, the peak value of the density profiles is a function of the ratio of the damping coefficient and the time scale of the shear transformation.

1. Nikolai V. Priezjev
Department of Mechanical and Materials Engineering
Wright State University
Movies, preprints @
http://www.wright.edu/~nikolai.priezjev/
Plastic deformation of a model glass induced by a local shear
transformation
N. V. Priezjev, “Plastic deformation of a model glass induced by a local shear transformation”,
Physical Review E 91, 032412 (2015); “The effect of a reversible shear transformation on
plastic deformation of an amorphous solid”, J. Phys.: Condens. Matter 27, 435002 (2015).
APS March 3, 2015
0

2. Time-dependent elastic response to a local shear transformation in 2D glass
Puosi, Rottler, Barrat, Phys. Rev. E 89, 042302 (2014).
Long-time mean displacement field
with quadrupolar symmetry
Instantaneously strain circular
inclusion into an ellipse (elementary
plastic event in deformed glasses)
Eshelby inclusion problem (1957)
1. Long-time response averages out to continuum solution despite large fluctuations
2. A crossover from a propagative transmission in the case of weakly damped
dynamics to a diffusive transmission for strong damping (large friction)

3. Details of molecular dynamics simulations and parameter values
Monomer density:  = A + B = 1.20  3
Temperature: T = 0.01 kB << Tg = 0.45 kB
System dimensions: 20.27σ  20.27σ  20.27σ
Periodic boundary conditions tMD= 0.005τ
Langevin
dynamics
Binary 3D Lennard-Jones Kob-Andersen mixture:





















612
4)(
rr
rVLJ




Kob & Andersen, Phys. Rev. E 51, 4626 (1995).
10000,,5.01.5,,0.1  pBABBABAA Nmm
,88.00.8,,0.1  BBABAA 
Interaction parameters for   A and B particles:
AAAAA m  
Oscillatory shear strain: )/sin()( 0 itt  
it 0Time scale of shear event:
Friction coefficient , duration of shear event i
135
Plastic deformation after reversible shear event
(averaged over 504 independent samples)
Inclusion
ri  3

4. Snapshots of cage jump configurations for different strain amplitudes o
1.00 
4.00 3.00 
2.00 
r
With increasing strain amplitude o, the number of cage jumps increases and they tend to
aggregate into compact clusters.
1
0.1 
 
Friction
coefficient
Radial density
profiles (r)?
0 Inclusion
ri  3

5. Radial density profiles of cage jumps (r) for different strain amplitudes o
Time scale of shear
transformation
The average density of cage jumps (r) becomes larger as the strain amplitude increases.
1
0.1 
 
Friction
coefficient
4.00 
4.00 
3.00 
3.00 
0
Inclusion
ri  3 05.00 

6. Radial density profiles of cage jumps (r) for different times of shear event i
1
0.1 
 
Friction
coefficient
3.00 
Strain
amplitude
The density of cage jumps increases with increasing shear transformation time scale i.
0

Inclusion
ri  3

7. Radial density profiles of cage jumps (r) for different friction coefficients 
3.00 
Strain
amplitude
With decreasing friction coefficient, the density of cage jumps increases
and it appears to saturate at small values of .
Inclusion
0

Inclusion
ri  3

8. Rescaled radial density profiles of cage jumps  for different i and 
3.00 
Strain
amplitude
The density profiles can be made to collapse onto a master curve for different
values of the friction coefficient  and the time scale of shear event i.
?
0

Inclusion
ri  3
max

9. Peak value of density profiles of cage jumps as a function of i and 
Log-log contour plot of the maximum of density profiles of cage jumps.
3.00 
Strain
amplitude
3
max
iln
const)/(max  i
Slope +1ln
1
~

 i
0
(frictioncoefficient)

10. For a given strain amplitude, the peak values of the cage density profiles collapse onto a
master curve as a function of the ratio /i : constant to power-law decay with the slope −0.65.
Maximum of density profiles of cage jumps as a function of /i
Rescale density peaks:
5
o
m
m


 
Saturation regime: large i
and weak damping
0
Small i and
strong damping

11. Angular dependence of the density profiles of cage jumps
The angle is θ = 0◦, 10◦, 20◦, 30◦, 40◦, 50◦, 60◦, 70◦, 80◦, 90◦ from top to bottom.
0

12. The probability distribution of cluster sizes of cage jumps
The strain amplitude is 0 = 0.05, 0.1, 0.15, 0.2, 0.3, and 0.4 from bottom to top.

13. Conclusions:
http://www.wright.edu/~nikolai.priezjev Wright State University
• Plastic deformation after reversible local shear transformation is studied using MD
simulations of the binary 3D Lennard-Jones Kob-Andersen mixture.
• It was found that, in general, the density of irreversible cage jumps increases with
increasing strain amplitude of the shear transformation.
• For a given strain amplitude o, the density of cage jumps increases upon either
increasing time scale of the shear event or decreasing friction coefficient.
• The peak values of the density profiles of cage jumps collapse onto master curves as
a function of /i : crossover from constant to power-law decay m  (/i )−0.65.
5
o
m
m


 
0
N. V. Priezjev, “Plastic deformation of a model glass induced by a local shear transformation”,
Physical Review E 91, 032412 (2015); “The effect of a reversible shear transformation on
plastic deformation of an amorphous solid”, J. Phys.: Condens. Matter 27, 435002 (2015).

14. Numerical algorithm for detection of cage jumps
Numerical algorithm for
detection of cage jumps:
Candelier, Dauchot,
Biroli, PRL (2009).