The linear Elasticity complex: a natural formulation

Abstract

We reformulate the Elasticity complex and Saint-Venant's compatibility condition using the generalized differential complex of Dubois-Violette-Henneaux. This is just a slight and natural modification of the de Rham complex to take account of the index symmetry of the tensors involved. An integrating formula to recover the displacement from the strain and similar to the Poincar{é} formula is provided. Finally, a Hodge star operator and a dual complex is introduced, which allows to recover stress potentials in dimensions 2 and 3.