A new formulation for the computation of inter-element forces and stresses

The paper describes a new technique for the determination of the inter-element forces and tractions computed at the corner nodes of a finite element mesh. The procedure, easily implementable as a postprocessing step, is based on the double minimization of an objective function representing the error between the inter-element stress tractions and the projection of the best-fit stress tensor T along the planes of the interfaces converging at an element corner point. The motivation for this work is the evaluation of inter-element stresses for a fracture simulation procedure in which each line of the mesh is a potential crack line, without the need for systematic use of interface elements and duplication of nodes. However, the proposed technique also turns out to be an efficient and accurate way for the computation of the stress state at the nodes in the standard displacement formulation of the FEM, and therefore it can be also used advantageously simply for smoothing purposes.