Boundary conditions resulting from cylindrical and longitudinal periodicities

Materials with patterned microstructures can be represented by a unit cell within which micromechanical stresses can be analysed. This approach, with accurate boundary conditions, allows huge savings to be made in computation time without affecting the accuracy of the results. In this paper, sets of boundary conditions for unit cells with periodicity in axial and circumferential directions are derived. These are verified by analysis of circular and hexagonal rods subjected to thermal loading, uniform tension or uniform torsion. The analysis of a thermal barrier coating system with a periodic oxide interface is presented as an application of the boundary conditions.