Estimation of computational homogenization error by explicit residual method

In this paper a new method is introduced for the estimation of modeling error resulting from homogenization of elastic heterogeneous bodies. The approach is similar to the well known explicit residual approximation error estimation. It is proved that besides the residuum of the equilibrium equation and interelement traction jump also a difference of stress divergences as well as traction jump along the material interfaces contribute to the modeling error estimate. Moreover, explicit specification and numerical evaluation of “stability” constants provide reasonable effectivity index of this error indicator.Selected numerical examples illustrate the promise of this approach. Therefore, the proposed methodology is a computationally inexpensive option for the other methods of modeling error assessment.