Research Article
Jun 1968
Stress Concentration in Strain-Gradient Bodies
Authors: Glenn A. Hazen and Yechiel WeitsmanAuthor Affiliations
Publication: Journal of the Engineering Mechanics Division
Volume 94, Issue 3
Abstract
An analytical solution is presented to a boundary-value problem in the linear elasticity in which potential energy depends on strains and strain gradients. The problem considered is that of an infinite medium, containing a spherical cavity, subjected to uniaxial tension at infinity. For an isotropic, centrosymmetric material, the strain-gradient theory contains five additional material constants (micro-constants), which may be related to Lame' constants by means of two material lengths. The range of the micro-constants is determined on the basis of positive definiteness of the potential energy, and under this condition no difficulty is encountered in reducing the strain-gradient solution to either the couple-stress or the classical solution. A reduction to the classical result does not have to employ the couple-stress solution as an intermediate step. Numerical calculations are performed for various values of nondimensionalized, independent parameters. The results show that, in contrast to predictions of couple-stress theory, the stress concentration factor can exceed the classical value.
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Published In
Journal of the Engineering Mechanics Division
Volume 94 • Issue 3 • June 1968
Pages: 773 - 795
Copyright
© 1968 American Society of Civil Engineers.
History
Published in print: Jun 1968
Published online: Feb 3, 2021
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Glenn A. Hazen
Asst. Prof., Dept. of Civ, Engrg., Ohio Univ., Athens, Ohio
Yechiel Weitsman
Assoc. Prof. of Applied Math., Brown Univ., Providence, R. I.
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