Stochastic approach to plasticity and yield in amorphous solids.

Area of Science:

• Materials Science
• Condensed Matter Physics
• Solid Mechanics

Background:

• Amorphous solids exhibit complex plastic behavior under strain.
• Understanding the probability distribution functions (PDFs) of plastic events is crucial for characterizing material response.

Purpose of the Study:

• To investigate the probability distribution function P(Δγ;γ) of strain intervals (Δγ) versus accumulated strain (γ) in amorphous solids.
• To explore the relationship between the strain interval PDF and the eigenvalue PDF of plastic modes.
• To determine the γ-dependence of these PDFs and identify transitions in material behavior.

Main Methods:

• Analysis of the probability distribution function P(Δγ;γ) for strain intervals (Δγ).
• Examination of the scaling behavior of the PDF tails as Δγ approaches zero.
• Relating the exponents of the strain interval PDF to those of the plastic mode eigenvalue PDF (P(λ)).

Main Results:

• The tail of P(Δγ;γ) scales as Δγ(η) as Δγ→0.
• The exponent η is linked to the eigenvalue PDF exponent θ by η=(θ-1)/2.
• Both PDFs P(Δγ;γ) and P(λ) are discontinuous functions of γ, exhibiting transitions at γ=0(+) and the yield point γ=γ(Y) in slowly quenched solids.

Conclusions:

• The probability distributions of strain intervals and plastic modes undergo discontinuous transitions during yielding.
• These transitions are dependent on the quenching rate, with quickly quenched solids showing a smeared transition.
• The study provides insights into the fundamental nature of plasticity and yielding in amorphous materials.