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On a Mechanical Model of the Bopp‐Podolsky Potential
Author(s) -
Günther H.
Publication year - 1976
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19764880605
Subject(s) - torsion (gastropod) , isotropy , physics , gravitational singularity , classical mechanics , singularity , continuum mechanics , geometry , quantum mechanics , mathematics , medicine , surgery
For an arbitrary given distribution of dislocations and disclinations the general state of stress of a mechanical continuum is investigated. The medium is reacting with stresses and momentum stresses (Cosserat continuum). By means of differential geometry it is shown that the deformations 0 ϵik and ϵ ik of two arbitrary materials with identical distributions of defects differ merely by a displacement field u i ( x r , t ). If 0 ϵik are the eigendeformations of an isotropic medium, then in the linear theory the field u i of a Cosserat continuum can be separated from 0 ϵik . If the problem is static the u i obey the potential equation of Bopp‐Podolsky electrodynamics. As source only torsion (dislocations and torsion of disclinations) is acting. To give an example the field u i for straight dislocations and disclinations is calculated. Especially the problem of singularities is discussed.