Another approach to linearized elasticity and Korn's inequality

Patrick Ciarlet (1) , Philippe G. Ciarlet

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

We describe and analyze an approach to the pure traction problem of three-dimensional linearized elasticity, whose novelty consists in considering the linearized strain tensor as the 'primary' unknown, instead of the displacement itself as is customary. This approach leads to a well-posed minimization problem, constrained by a weak form of the St Venant compatibility conditions. It also provides a new proof of Korn's inequality.

Patrick Ciarlet, Philippe G. Ciarlet. Another approach to linearized elasticity and Korn's inequality. Comptes Rendus. Mathématique, 2004, 339 (4), pp.307-312. ⟨10.1016/j.crma.2004.06.021⟩. ⟨hal-00988265⟩