Manifolds in a theory of microstructures

G. Capriz, R. J. Knops

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A synopsis, broadly based on contributions by Capriz and co-workers, is presented of a model for a body with microstructure that employs the Cartesian product of a Euclidean space (a fit set part of which is instantaneously occupied by the gross image of the body) and a Riemannian manifold each of whose members specifies a microstructure. Motivation is provided by known special theories. Macro and micro kinetic energy, kinetic coenergy, and inertia are discussed preparatory to the derivation of the governing nonlinear partial differential equations from the Lagrangian action principle, Noether’a theorem, and a Hamiltonian formulation. Precise mathematical specification of initial and boundary conditions remains fragmentary.

Original languageEnglish
Title of host publicationDifferential Geometry and Continuum Mechanics
Editors Gui-Qiang G. Chen, Michael Grinfeld, R. J. Knops
PublisherSpringer International Publishing
Pages167-201
Number of pages35
Volume3
ISBN (Electronic)978-3-319-18573-6
ISBN (Print)978-3-319-18572-9
DOIs
Publication statusPublished - 2015
EventDifferential Geometry and Continuum Mechanics 2013 - Edinburgh, United Kingdom
Duration: 17 Jun 201321 Jun 2013

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer International Publishing
Volume137
ISSN (Print)2194-1009

Conference

ConferenceDifferential Geometry and Continuum Mechanics 2013
CountryUnited Kingdom
CityEdinburgh
Period17/06/1321/06/13

ASJC Scopus subject areas

  • Mathematics(all)

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