University of Illinois Urbana-Champaign

Conservation laws in elasticity of j-integral type

Chen, Francis H.K.; Shield, R.T.

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https://hdl.handle.net/2142/112141

Description

Title
Conservation laws in elasticity of j-integral type
Author(s)
  • Chen, Francis H.K.
  • Shield, R.T.
Issue Date
1976-03
Keyword(s)
  • Elasticity
  • J-integral Type
  • Conservation Laws
  • Strain Energies
Abstract
Conservation laws which are expressible as functionals linear in the strain energy and its derivatives are laws of the same type as the J-integral. For finite elastic deformations of homogeneous bodies, relations between the conservation laws are shown through the use of inverse deformation results. Completeness of the laws are established for homogeneous materials and for materials whose strain -energies satisfy objectivity, isotropy, or are homogeneous functions. Laws for a class of membranes inflated by pressure are derived and applied to a cylindrical membrane. For infinitesimal deformations of linear elastic bodies, new laws which relate two independent equilibrium states are presented and applied to the problem of a line crack in a plate under mixed-mode loading conditions . A relation is shown to exist between the J-integral and the reciprocal work theorem of Betti.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 407
  • 1976-6002
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112141
Sponsor(s)/Grant Number(s)
National Science Foundation 76/03 NSF GK 37539 76/03
Copyright and License Information
Copyright 1976 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.