Stability of an expanding circular cavity and the failure of amorphous solids

Eran Bouchbinder, Ting-Shek Lo, Itamar Procaccia, and Elad Shtilerman
Phys. Rev. E 78, 026124 – Published 28 August 2008

Abstract

Recently, the existence and properties of unbounded cavity modes, resulting in extensive plastic deformation failure of two-dimensional sheets of amorphous media, were discussed in the context of the athermal shear-transformation-zones (STZ) theory. These modes pertain to perfect circular symmetry of the cavity and the stress conditions. In this paper we study the shape stability of the expanding circular cavity against perturbations, in both the unbounded and the bounded growth regimes (for the latter the unperturbed theory predicts no catastrophic failure). Since the unperturbed reference state is time dependent, the linear stability theory cannot be cast into standard time-independent eigenvalue analysis. The main results of our study are as follows: (i) sufficiently small perturbations are stable; (ii) larger perturbations within the formal linear decomposition may lead to an instability; this dependence on the magnitude of the perturbations in the linear analysis is a result of the nonstationarity of the growth; and (iii) the stability of the circular cavity is particularly sensitive to perturbations in the effective disorder temperature; in this context we highlight the role of the rate sensitivity of the limiting value of this effective temperature. Finally we point to the consequences of the form of the stress dependence of the rate of STZ transitions. The present analysis indicates the importance of nonlinear effects that were not taken into account yet. Furthermore, the analysis suggests that details of the constitutive relations appearing in the theory can be constrained by the modes of macroscopic failure in these amorphous systems.

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  • Received 11 November 2007

DOI:https://doi.org/10.1103/PhysRevE.78.026124

©2008 American Physical Society

Authors & Affiliations

Eran Bouchbinder1,2, Ting-Shek Lo1,3, Itamar Procaccia1, and Elad Shtilerman1

  • 1Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
  • 2Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
  • 3Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong

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Vol. 78, Iss. 2 — August 2008

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