Stochastic approach to plasticity and yield in amorphous solids

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
H G E HentschelSrikanth Sastry

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〉 ...Continue Reading

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Citations

Dec 18, 2019·Proceedings of the National Academy of Sciences of the United States of America·Baoshuang ShangJean-Louis Barrat
Sep 10, 2020·Soft Matter·Céline Ruscher, Jörg Rottler
Mar 12, 2016·Physical Review Letters·Awadhesh K DubeyMurari Singh
Mar 12, 2016·Physical Review Letters·Prabhat K JaiswalMurari Singh
Jan 20, 2018·Physical Review. E·Jie Lin, Wen Zheng
Aug 6, 2016·Physical Review Letters·Sylvain PatinetMichael L Falk
Sep 19, 2020·Physical Review. E·P ZhangL Truskinovsky
May 20, 2018·Physical Review. E·Armand BarbotSylvain Patinet
Apr 16, 2020·Physical Review. E·Geert KapteijnsEdan Lerner
Jan 20, 2018·Physical Review. E·Jishnu N NampoothiriBulbul Chakraborty
Apr 3, 2019·Physical Review. E·Wencheng JiMatthieu Wyart
Jan 5, 2021·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Ezequiel E Ferrero, E A Jagla
Mar 10, 2021·The Journal of Chemical Physics·Corrado RainoneEdan Lerner

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