An extended semi-analytical formulation for fast and reliable mode I/II stress analysis of adhesively bonded joints

The Finite Element (FE) method is able to address the stress analysis of adhesively bonded joints. However, analyses based on FE models are computationally expansive and it would be profitable to develop simplified approaches enabling extensive parametric studies. Firstly, a 1D-beam simplified model for the bonded joint stress analysis assuming a linear elastic adhesive material is presented. This model, derived from an approach inspired by the Finite Element (FE) method and based on the semi-analytical formulation of a 4-nodes macro-element, is able to simulate entire bonded overlaps at low computational costs. Secondly, a numerical procedure allowing for non-linear adhesive stress-strain relationships to be accounted for is presented. This procedure allows for various non-linear adhesive behaviors (ie. softening, plastic, etc.) to be accounted for with no restriction on the specimen geometry. The possible mixed-mode I/II response of the adhesive layer is introduced through an extension of the classical Cohesive Zone Modeling (CZM) procedure. The aforementioned procedure is then illustrated using a bi-linear softening adhesive behavior. However the procedure is not limited to this particular behavior only. The results obtained are finally compared to those of more time-consuming 2D FE strength predictions. Good agreement is shown.