A new mixed finite element has been developed for the analysis of bonding problems. The element has been derived from the mixed variational principle for the combined mixed functional subject to a bonding condition. Therefore, the present mixed model has been composed of a mixed element based on the combined mixed functional and a bonding element derived from the bonding condition. Since the bilinear form of the combined mixed functional is V-elliptic or weakly coercive, the variational problem associated with the functional has a unique solution and linear constraints can be successfully incorporated into the functional in terms of Lagrange multipliers. Moreover the mixed element based on the functional has no spurious zero energy modes regardless of selecting the approximating polynomials of the independent field variables if the completeness and the continuity are satisfied. Thus, more desirable and practical approximations, such as a continuous linear stress and quadratic displacement approximation, are possible in the mixed model without any cost. For the elastic bonding problem, the present mixed model satisfies equilibrium equation, the displacement and the traction boundary condition, and the interfacial traction continuity condition, while the displacement based model violates the interfacial traction continuity condition. Therefore, the displacement based model would result in considerable amount of error along the bonding surface of a composite structure of highly dissimilar materials, while the mixed model would give reliable solutions along the interface. In order to show the accuracy and the applicability of the proposed mixed model, composite structures, having low or high stress gradient along the bonding interface, have been analyzed. For the structures with low stress gradient, the results of the mixed model with both a continuous and a discontinuous stress approximation have been in close agreement with those of the analytic solution. On the other hand, for the problems with high stress gradient, the results of the model with the continuous stress interpolation have been in close agreement with those available in the literature, while the model with discontinuous stress interpolation has resulted in considerable amounts of discrepancies near the free edge. From the confirmation of the mixed model, it has been applied to the dental implant shape design problem. Both the shape effect of an angled neck and the material effect of body of typical dental implants on the interface stress distribution at the alveolar bone have been examined. The bonding stress level of the inner slanted shape implant has been lower than that of the straight or the outer slanted shape implant. The material changes of implant body has had negligible effect on the interface stress.
