Special finite elements for modelling adhesively bonded joints in two- and three-dimensions

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Virginia Tech


Special methods were developed to model adhesively bonded joints in two- and three- dimensions using a simple finite element approach. Analysis of a two-dimensional bonded joint is performed by using plane frame elements to model the adherends, and a single plane elasticity-type element through the thickness of the adhesive bondline. A similar approach was developed for the analysis of bonded joints in three-dimensions such that the adherends were modelled by shear deformable plate elements, and the adhesive as a single solid element through the thickness. The degrees of freedom of both the plane elasticity ADH2D element and the solid ADH3D element are offset from their respective surfaces to the nodes of the adherend elements in each case, such that displacement continuity is achieved at element interfaces. The ADH3D-plate formulation can be used to analyze tapered adhesive layers, stepped laminated composite adherends, and thermal and moisture expansion effects in both the adhesive and adherends.

A single lap shear joint was modelled in both two- and three-dimensions using the ADH2D-plane frame, and the ADH3D-plate configurations respectively. Adhesive stresses in two-dimensions converged to accepted closed-form solutions. Significant three-dimensional effects were observed in the ADH3D results, and possible explanations for this behavior were given. A typical crack-patch repair scenario was also modelled in two- and three-dimensions using the ADH3D formulation. The use of appropriate boundary and loading conditions for modelling such applications were discussed. Adhesive joints can be accurately and efficiently modelled using the ADH2D-plane frame, and the ADH3D-plate methods.

In the process of selecting the most appropriate element to model the adherends in the three-dimensional ADH3D formulation, the phenomenon of shear locking in plate finite elements was examined and explained in terms of the presence of boundary layer-type solutions to the equations of shear deformable plate theory. To demonstrate this, the governing equations of Reissner plate theory were derived and reduced to independent equations expressed in terms of a displacement potential φ and a rotational stream function ψ. A plate finite element was derived using an interpolation of the displacement potential φ. Shear-locking was not observed when square plates with simply-supported and clamped edges were modelled using this finite element. A discussion on the actual cause of shear-locking and recommendations for future development and implementation of the concepts in this study were made.