Transcript Presentation

Statistical Physics of Plasticity in Amorphous Solids with
Implications to the Glass Transition
Itamar Procaccia
The Weizmann Institute of Science
Rehovot, 76100 Israel
Work with: Smarajit Karmakar and Edan Lerner
StatPhys L’viv July 4, 2012
Glass phenomenology
The carriers of plasticity in crystalline materials
Glasses are disordered like liquids
Crystalline vs. glassy response to stress
What is known about plasticity in amorphous
solids?
Long tradition starting with Argon, Spaepen, Langer
led to the STZ theory. Basic assumptions:
• There exist STZ in the material.
• Plastic events include a small number of
particles (30-100)
• Plastic events are statistically uncorrelated
So what is plasticity in amorphouas solids?
Typical stress-strain and energy-strain
curves in AQS systems
  
V
U 

2
Statistics of Plastic Drops in the steady state
   1
In the equilibrium state the probability to see zero energy
barrier is zero, but NOT in the steady state
Weibull’s theorem: in N random samples the minimal value
observed is
,
In the elasto-plastic state the probability to see zero energy
barrier is not zero!
1/N
During a `mechanically stable’ trajectory
How to find the distribution of plastic modes
in the thermodynamic limit?
The statistics of minimal values
Weibull’s theorem: in N random samples the
minimal value observed is
,
A very important conclusion
First method: configurational entropy
Second method: Finite Size Scaling
Thank you!