Direct Computation of Stresses in Elasticity

We describe and analyze an approach to the pure Neumann problem of three-dimensional linearized elasticity, whose novelty consists in considering the strain tensor field as the sole unknown, instead of the displacement vector field as is customary. This approach leads to a well-posed quadratic minimization problem of a new type, constrained by a weak form of the classical Saint Venant compatibility conditions. Interestingly, this approach also provides a new proof of Korn’s inequality.