Boundary conditions resulting from cylindrical and longitudinal periodicities

• Unit cell boundary conditions are derived for axial and circumferential periodicity.
• This rigorous framework for unit cell modelling avoids pitfalls of intuitive methods.
• The boundary conditions are validated for several circular and prismatic problems.
• The boundary conditions are used in a model of a thermal barrier coating interface.
• Models using the present boundary conditions agree closely with reference solutions.

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.