Emergence of linear isotropic elasticity in amorphous and polycrystalline materials

Shivam Mahajan, Joyjit Chattoraj, and Massimo Pica Ciamarra
Phys. Rev. E 103, 052606 – Published 10 May 2021

Abstract

We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale ξE, so that the central limit theorem dictates the emergence of continuum linear isotropic elasticity on increasing the specimen size. The stiffness matrix of systems of finite size L>ξE is obtained, adding to that predicted by linear isotropic elasticity a random one of spectral norm (L/ξE)3/2 in three spatial dimensions. We further demonstrate that the elastic length scale corresponds to that of structural correlations, which in polycrystals reflect the typical size of the grain boundaries and length scales characterizing correlations in the stress field. We finally demonstrate that the elastic length scale affects the decay of the anisotropic long-range correlations of locally defined shear modulus and shear stress.

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  • Received 10 February 2021
  • Accepted 22 April 2021

DOI:https://doi.org/10.1103/PhysRevE.103.052606

©2021 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Polymers & Soft MatterGeneral PhysicsStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Shivam Mahajan1, Joyjit Chattoraj1,2, and Massimo Pica Ciamarra1,3,*

  • 1Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
  • 2Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore 138632, Singapore
  • 3CNR–SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126, Napoli, Italy

  • *massimo@ntu.edu.sg

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Issue

Vol. 103, Iss. 5 — May 2021

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