Cauchy elasticity with dislocations in the small strain assumption

In this letter it is shown how the singularities created by dislocations in an elastic body must not preclude from a linear approach. Cauchy elasticity is considered and hence no variational approach is needed and the displacement field only appears in a second step, as an interpretation of the one...

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Bibliographic Details
Published in:Applied mathematics letters 2015-08, Vol.46, p.94-99
Main Author: Van Goethem, Nicolas
Format: Article
Language:English
Subjects:
Beltrami decomposition
Dislocations
Elasticity
Helmholtz decomposition
Incompatibility operator
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Summary:In this letter it is shown how the singularities created by dislocations in an elastic body must not preclude from a linear approach. Cauchy elasticity is considered and hence no variational approach is needed and the displacement field only appears in a second step, as an interpretation of the one of the two model variables, arisen from a Beltrami decomposition of the strain tensor. The second model variable obeys nonclassical PDEs relying on the incompatibility operator, and whose well posedness is here addressed.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2015.02.012