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

Daniela Ciancio (1) , Ignacio Carol (2) , Massimo Cuomo (3)

1 School of Civil and Resource Engineering
2 School of Civil Engineering
3 Dipartimento di Ingegneria Civile ed Ambientale

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.

Domaines: Mécanique [physics.med-ph]

Daniela Ciancio, Ignacio Carol, Massimo Cuomo. On inter-element forces in the FEM-displacement formulation, and implications for stress recovery. International Journal for Numerical Methods in Engineering, 2006, 66 (3), pp.502-528. ⟨hal-00878256⟩