Abstract:

Elasticity-based solutions to unit cell boundary-value problems are potentially attractive alternatives to the finite-element or finite-volume based approaches due to orders-of-magnitude improvements in efficiency, portability and user friendliness. These features enable potentially widespread use of elasticity-based homogenization techniques in different branches of engineering and applied science. A major impediment to the development and implementation of such techniques, however, is the inseparable character of the elastic boundary-value problem wherein satisfaction of continuity and boundary conditions in different coordinate systems is required. Herein, we examine a recently developed locally-exact homogenization theory for periodic materials with respect to the efficiency of different manner of periodic boundary condition application, including collocation, weighted least squares and variational approaches. A new approach is then proposed based on an optimization algorithm which enables efficient identification of convergent eigenfunction eigenvectors for the unit cell displacement field representation.