A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.
"A Simple Circular Cell Method for Multilevel Finite Element Analysis." J. Appl. Math. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/526846