ANALYSIS OF THE INCOMPATIBILITY OPERATOR AND APPLICATION IN INTRINSIC ELASTICITY WITH DISLOCATIONS

Samuel Amstutz (1, 2) , Nicolas van Goethem (3)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie
2 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
3 CMAF - Centro de Matemática e Aplicações Fundamentais

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.

Mots clés: incompatibility; dislocations; intrinsic elasticity; Sobolev spaces; lifting; transmission conditions

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Samuel Amstutz, Nicolas van Goethem. ANALYSIS OF THE INCOMPATIBILITY OPERATOR AND APPLICATION IN INTRINSIC ELASTICITY WITH DISLOCATIONS. SIAM Journal on Mathematical Analysis, 2016, 48 (1), pp.320-348. ⟨hal-01150071v2⟩