The local response in structures using the Embedded Unit Cell Approach

•Development of a new concept, the embedded unit cell (EUC) approach.•The EUC formulation is not restricted to the homogenization periodic assumptions.•Solution of stress concentration problems through classical homogenization formulation.•The EUC is reduced computational cost model.

This paper presents the development of a new concept, the Embedded Unit Cell (EUC) approach, to calculate local responses in elastic media. The EUC approach is based on a multi-scale formulation of non-periodic domains to evaluate the local/micro response where stress concentrations are expected. The formulation is based on alternative boundary conditions which is not restricted to periodic assumptions of the unit cell response that is required in the classical theory. This approach provides a reduced computational cost model of the macroscopic/global problem while preserving the accuracy at the microscale problem. We conclude with a numerical verification study.