Bonded Joint Elements for Structural Modeling and Failure Prediction

Elements based on the exact stiffness matrix method contain an embedded analytical solution that can capture detailed local fields, enabling more efficient mesh independent finite element analysis. In the present study, this method was applied to adhesively bonded joints. The adherends were modeled as Euler-Bernoulli beams, and the adhesive layer was modeled as a bed of linear shear and normal springs. The field equations were derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields were used to generate shape functions and a stiffness matrix for a single joint finite element. Additionally, the capability to model non-linear adhesive and adherend constitutive behavior was developed, and progressive failure of the adhesive was modeled by using a strain-based failure criteria and re-meshing the joint as the adhesive fails. Example joint configurations were analyzed to demonstrate element convergence and the modeling of functionally graded adhesives.