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On inter‐element forces in the FEM‐displacement formulation, and implications for stress recovery

This paper describes a new technique for the determination of the inter‐element forces and tractions, as well as stress state at nodes, as a post‐processing step after the solution of standard FE‐displacement calculation. The work is motivated in the context of a broader development of a procedure to simulate fracture processes using a discrete approach without the need of double‐noded interface elements. The technique, easily implementable, 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 node. The formulation is illustrated with some basic examples in which the resulting stress tensors and inter‐element forces are compared to theoretical solutions and to the results obtained by using a traditional stress average smoothing method. Copyright © 2005 John Wiley & Sons, Ltd.