Homogenization of mechanical and thermal stresses in functionally graded adhesive joints

In recent years, functionally graded adhesives (FGAs) have been developed and successfully applied with the objective to reduce the stress concentrations occurring in bonded joints and to exploit their full lightweight design potential. The present work provides a computational framework based on a general predictive analytical model for FGA joints with composite adherends under mechanical and thermal loading embedded in an optimization procedure. In this way, an optimal homogenization of the adhesive stresses using FGAs is achieved. The proposed analysis approach follows the idea of general sandwich-type analyses and is thus applicable to various adhesive joint configurations as e.g. single lap joints, L-joints, T-joints, reinforcement patches and even balanced double lap joints. For the case of homogeneous adhesives, closed-form analytical solutions are presented and compared to existing solutions in literature. The predicted adhesive stress distributions of several FGA joint configurations are studied and compared to numerical results of finite element analyses where a good agreement is obtained. Moreover, a comprehensive study regarding the optimized functional grading for two particular joint configurations is performed and discussed. The corresponding grading functions are obtained solving an underlying optimization problem that minimizes a predefined objective function characterized by an equivalent stress quantity.