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 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.

• Type: Journal
• Year: 2016
• Where: SIAMMA
• Authors: Samuel Amstutz, Nicolas Van Goethem
• Keywords: Computer Graphics, SIAMMA 2016