Analysis of the Incompatibility Operator and Application in Intrinsic Elasticity with Dislocations

The incompatibility operator arises in the modeling of elastic materials with dislocations and in the intrinsic approach to elasticity, where it is related to the Riemannian curvature of the elastic metric. It consists of applying successively the curl to the rows and the columns of a 2nd-rank tenso...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2016-01, Vol.48 (1), p.320-348
Main Authors: Amstutz, Samuel, Van Goethem, Nicolas
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
Optimization and Control
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Summary:The incompatibility operator arises in the modeling of elastic materials with dislocations and in the intrinsic approach to elasticity, where it is related to the Riemannian curvature of the elastic metric. It consists of applying successively the curl to the rows and the columns of a 2nd-rank tensor, usually chosen symmetric and divergence free. This paper presents a systematic analysis of boundary value problems associated with the incompatibility operator. It provides answers to such questions as existence and uniqueness of solutions, boundary traces lifting and transmission conditions. Physical interpretations in dislocation models are also discussed, but the application range of these results exceed by far any specific physical model.
ISSN:0036-1410
1095-7154
DOI:10.1137/15M1020113