Closed-form solutions for modellingthe response of adhesively bonded joints under thermal loading through exponential softening laws

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10 Citations (Scopus)


The bonding technique has received extensive attention in the recent decades. Unlike the use of metallic screws, screws or rivets, some of the advantages of this bonding technique include the elimination of stress concentration, lighter weight and the extension of the life cycle of the adhesively bonded structures. The stiffness and strength of a material are increased after bonding with another reinforced material, but it can only be effective if the interface is able to transfer bond stresses. However, how the bond stress transfer is carried out when the joint, reinforcement and substrate are subjected to a thermal loading is not yet well understood. One way to facilitate and improve such knowledge is to develop analytical solutions that, despite their simplicity, allow parameters to be identified that may directly influence the bond between materials. Therefore, the present study aims to develop a series of closed-form solutions able to describe the debonding process of bonded joints with different characteristics using two different exponential softening laws. The results mainly describe the interfacial slips, bond stresses and strains in both materials during the temperature increase process. In total, 108 examples with different bonding conditions are studied and, at the same time, numerically modelled through the Finite Element Method (FEM). The numerical results were compared to the proposed closed-form solutions and a satisfactory agreement was obtained between the numerical and analytical results, validating the latter. When considered in the simulations, the glass transition temperature (Tg) of the adhesive greatly affected the bond stress transfer between materials and compromising the initial integrity of the adhesively bonded structure.

Original languageEnglish
Article number103527
JournalMechanics of Materials
Publication statusPublished - Sep 2020


  • Bonded joints
  • Finite element analysis
  • Non-linear analytical model
  • Temperature


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