A general formulation of an analytical model for the elastic–plastic behaviour of a spot weld finite element

• We increase the SWE applicability to cases where the load is over the elastic limit.
• We present an extension of this analytical model by introducing a parametric law.
• We highlight the influence of constrained edge to the plastic behaviour of the plate.
• This distinction allows to address the plasticization effort to the “main link” of SWE.
• Results of plates with SWE are compared to those obtained with shell elements.

A general formulation of an analytical procedure for the evaluation of the elastic–plastic behaviour of spot welded joints is presented. The procedure is based on a model of spot weld region shaped by a circular plate having variable thickness and having a central rigid nugget representing the spot weld. A closed form solution of the original analytical approach allows to define the displacement of the rigid nugget, when an axial load is applied on the plate, though plasticity and large displacements are present. The so defined spot weld region model has to be used as the basis to extend the capability of a spot weld element in FE analysis when plasticity and large displacements are in effect. As well as presented in previous works, the procedure is completely general; the accuracy on geometrical parameters dependency is now improved and the strain hardening material characteristics has been introduced.Furthermore the constraints influence of the sheet metal surrounding the spot on elastic–plastic behaviour is investigated and evaluated, in order to generalize the plastic contribution on spot weld stiffness. Even if the theoretical framework is non-trivial, the formulation of the proposed procedure is straightforward and it can be easily implemented as an add-on of a FE code.The results, obtained by applying the general analytical procedure to some examples of spot welded joints, precisely match those obtained modelling spot weld region by FEA.