Geometry and mechanics of two-dimensional defects in amorphous materials

Michael Moshe, Ido Levin, Hillel Aharoni, Raz Kupferman, Eran Sharon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We study the geometry of defects in amorphous materials and their elastic interactions. Defects are defined and characterized by deviations of the material's intrinsic metric from a Euclidian metric. This characterization makes possible the identification of localized defects in amorphous materials, the formulation of a corresponding elastic problem, and its solution in various cases of physical interest. We present a multipole expansion that covers a large family of localized 2D defects. The dipole term, which represents a dislocation, is studied analytically and experimentally. Quadrupoles and higher multipoles correspond to fundamental strain-carrying entities. The interactions between those entities, as well as their interaction with external stress fields, are fundamental to the inelastic behavior of solids. We develop analytical tools to study those interactions. The model, methods, and results presented in this work are all relevant to the study of systems that involve a distribution of localized sources of strain. Examples are plasticity in amorphous materials and mechanical interactions between cells on a flexible substrate.

Original languageAmerican English
Pages (from-to)10873-10878
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number35
StatePublished - 1 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015, National Academy of Sciences. All rights reserved.


  • Amorphous solid
  • Defects
  • Elasticity
  • Plasticity
  • Reference metric


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