Multiscale simulation of particle-reinforced elastic–plastic adhesives at small strains

Many aerospace, aircraft or automotive mechanical components are joined together by using a structural adhesive. Adherend-to-adherend joint performance is usually carried out by a thin adhesive layer such that loads are transferred through this region, being then a critical point in the design. In order to ensure a proper behaviour of the adhesive under dynamical, mechanical, thermal or rheological loads, they are typically reinforced with a second phase stiffer material in addition to the adhesive matrix. Due to the intrinsic nature of the matrix, it may be approached using an elastic–plastic behaviour. Under these circumstances the adhesive inherently shows a heterogeneous microstructure whereas the loads are applied at the macroscopic adherend scale. In this work, a multiscale formulation is developed to analyze particle-reinforced adhesive joints. The adherend and the adhesive region, which is modelled using cohesive elements, stand macroscopically. On the other hand, the macroscopic adhesive behaviour is obtained by a direct analysis of the two-distinguished phases interaction at the microscopic level, using micromechanics and homogenization. The presented approach provides macroscopic as well as microscopic information about load distribution avoiding phenomenological lab fitting, case to case, of the overall macroscopic behaviour of the adhesive.