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Title:Conservation laws in elasticity of j-integral type
Author(s):Chen, Francis H.K.; Shield, R.T.
Subject(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.
Issue Date:1976-03
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 407
1976-6002
Genre:Technical Report
Type:Text
Language:English
URI:http://hdl.handle.net/2142/112141
ISSN:0073-5264
Sponsor:National Science Foundation 76/03 NSF GK 37539 76/03
Rights Information:Copyright 1976 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04


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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    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.

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