Regular and Singular Dislocations

Marcelo Epstein, Reuven Segev

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

The theory of continuous distributions of dislocations and other material defects, when formulated in terms of differential forms, is shown to comprise also the discrete, or singular, counterpart, in which defects are concentrated on lower dimensional regions, such as surfaces, lines, and points. The mathematical tool involved in this natural transition is the theory of de Rham currents, which plays in regard to differential forms the same role as the theory of Schwartz distributions plays with respect to ordinary functions. After a review of the main mathematical aspects, the theory is illustrated with a profusion of examples and applications.
Original languageEnglish
Title of host publicationGeometric Continuum Mechanics
EditorsReuven Segev, Marcelo Epstein
Place of PublicationCham
PublisherSpringer International Publishing AG
Pages223-265
Number of pages43
ISBN (Print)978-3-030-42683-5
DOIs
StatePublished - 2020

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