Two- and three-dimensional geometrical nonlinear finite elements for analysis of adhesive joints

Special two- and three-dimensional adhesive elements have been developed for stress and displacement analyses in adhesively bonded joints. Both the 2-D and 3-D elements are used to model the whole adhesive system: adherends and adhesive layer. In the 2-D elements, adherends are represented by Bernoulli beam elements with axial deformation and the adhesive layer by plane stress or plane strain elements. The nodes of the plane stress–strain elements that lie in the adherend–adhesive interface are rigidly linked with the nodes of the beam elements, resulting in the offset nodes which coincide with the midplanes of the adherends. The 3-D elements consist of shell elements that represent the adherends and solid brick elements to model the adhesive. This technique results in smaller models with faster convergence than conventional 3-D finite element models. The resulting mesh can represent arbitrary beam- or plate-like geometries, which are a large part of adhesive joint designs. This model can include debonds as well as cracks within the adhesive, therefore it can be used for durability analysis of adhesive joints. Since large displacements are often observed in adhesively bonded joints, geometric nonlinearity is modeled. 2-D and 3-D stress analyses of single lap joints are presented. Important 3-D effects can be appreciated. A stress analysis of a crack patch geometry is presented.