Boundary conditions for unit cells from periodic microstructures and their implications

The most important aspect of formulating unit cells for micromechanical analysis of materials of patterned microstructures is the derivation of appropriate boundary conditions for them. There is lack of a comprehensive account on the derivation of boundary conditions in the literature, while the use of unit cells in micromechanical analyses is on an increasing trend. This paper is devoted to the generation of such an account, where boundary conditions are derived entirely based on considerations of symmetries which are present in the microstructure. The implications of the boundary conditions used for a unit cell are not always clear and therefore have been discussed. It has been demonstrated that unit cells of the same appearance but subject to boundary conditions derived based on different symmetry considerations may behave rather differently. One of the objectives of the paper is to inform users of unit cells that to introduce a unit cell one needs not only mechanically correct boundary conditions but also a clear sense of the microstructure under consideration. Otherwise the results of such analyses could mislead.