Kink band and shear band localization in anisotropic perfectly plastic solids

Thomas J. Nizolek*, Tresa M. Pollock, Robert M. McMeeking

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


Shear-driven strain localization has been observed in a wide variety of materials and may take the form of shear bands or kink bands. Based on observations of kink bands in plastically anisotropic metallic nanolaminates and single crystal metals, we posit that, for the specific case of isochoric deformation, the kinematics of kink band formation are indistinguishable from those of plane strain shear band formation. The only distinction between shear bands and kink bands in these systems would then be that kink bands ‘lock up’ at a particular value of material rotation while shear bands may progress to arbitrarily high strains. In order to investigate whether strong material anisotropy is sufficient to arrest shear localization at a geometry that matches the classic kink band geometry, we model the development of a band of simple shear within an anisotropic perfectly plastic material. The resulting analytical model provides the stress state needed to maintain the kinematics of simple shear as a function of material anisotropy, deformation band orientation, and shear strain (or equivalently, material rotation). It is found that plastic anisotropy can promote either kink band or shear band formation depending on the loading orientation. When the deviatoric stress is positive parallel to the plane of anisotropy, shear localization may progress without bound and a shear band is produced. When the deviatoric stress is negative parallel to the plane of anisotropy, shear localization is arrested after a certain material rotation, resulting in a kink band. Examination of the requisite applied stress state during kink band formation provides an explanation for the experimentally-observed ‘lock up’ geometry. Solutions for the band boundary inclination angle are obtained and used to provide bounds on permissible band angles for both shear bands and kink bands.

Original languageEnglish
Article number104183
Number of pages17
JournalJournal of the Mechanics and Physics of Solids
Early online date28 Oct 2020
Publication statusPublished - 31 Jan 2021

Bibliographical note

We sincerely wish to thank our reviewers for their helpful suggestions, and for prompting us to expand our analysis of the applied stress state. T.J.N. was supported by the Department of Defense through the National Defense Science and Engineering Graduate Fellowship as well as the Department of Energy through the Los Alamos Agnew National Security Fellowship. TMP acknowledges the support of DOE NNSA Grant DE-NA0003857. This work was supported in part by a Los Alamos National Laboratory Directed Research and Development (LDRD) Project 20200182DR. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract number 89233218NCA000001.


  • Anisotropic material (B)
  • Ideally plastic material (B)
  • Layered material (B)
  • Shear localization


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