title: Stochastic approach to plasticity and yield in amorphous solids.
abstract: We focus on the probability distribution function (PDF) P(Δγ;γ) where Δγ are the measured strain intervals between plastic events in a athermal strained amorphous solids, and γ measures the accumulated strain. The tail of this distribution as Δγ→0 (in the thermodynamic limit) scales like Δγ(η). The exponent η is related via scaling relations to the tail of the PDF of the eigenvalues of the plastic modes of the Hessian matrix P(λ) which scales like λ(θ), η=(θ-1)/2. The numerical values of η or θ can be determined easily in the unstrained material and in the yielded state of plastic flow. Special care is called for in the determination of these exponents between these states as γ increases. Determining the γ dependence of the PDF P(Δγ;γ) can shed important light on plasticity and yield. We conclude that the PDF's of both Δγ and λ are not continuous functions of γ. In slowly quenched amorphous solids they undergo two discontinuous transitions, first at γ=0(+) and then at the yield point γ=γ(Y) to plastic flow. In quickly quenched amorphous solids the second transition is smeared out due to the nonexisting stress peak before yield. The nature of these transitions and scaling relations with the system size dependence of 〈Δγ〉 are discussed.
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.|Department of Physics, Emory University, Atlanta, Georgia, United States.
authors.forename: H G E
authors.initials: HG
authors.lastname: Hentschel
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Prabhat K
authors.initials: PK
authors.lastname: Jaiswal
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Itamar
authors.initials: I
authors.lastname: Procaccia
authors.affiliation: Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bangalore 560064, India.
authors.forename: Srikanth
authors.initials: S
authors.lastname: Sastry