Finite-temperature mechanical instability in disordered lattices

Leyou Zhang and Xiaoming Mao
Phys. Rev. E 93, 022110 – Published 8 February 2016

Abstract

Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered systems. We use this theory to study two disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice. These two lattices belong to two different universality classes as they approach mechanical instability at T=0. We show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as GT1/2, whereas the square lattice shows GT2/3. We discuss generic scaling laws for finite-T mechanical instabilities and relate them to experimental systems.

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  • Received 18 March 2015
  • Revised 9 October 2015

DOI:https://doi.org/10.1103/PhysRevE.93.022110

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Leyou Zhang and Xiaoming Mao

  • Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

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Issue

Vol. 93, Iss. 2 — February 2016

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