Interval and subinterval homogenization-based method for determining the effective elastic properties of periodic microstructure with interval parameters

The main issue of this paper is to present an interval homogenization-based method (IHM) for the estimation of the effective elastic tensor for microscopic material properties with interval uncertainty. Based on the finite element method (FEM) for homogenization analysis, the interval effective elastic tensor is expanded by the first or second-order Taylor series for obtaining its upper and lower bounds. In order to guarantee the accuracy of IHM, the subinterval technique is introduced into the IHM for estimating the effective elastic tensor. Numerical examples of a unit rectangular voids cell and a unit particle filled polymers cell are implemented. Through comparing the numerical results with the results obtained by the Monte-Carlo simulation, the effectiveness and the efficiency of the IHM for homogenization analysis with interval uncertainty are verified. The influence of the microscopic interval uncertainty in material properties on a homogenized macroscopic elastic property of an inhomogeneous material has also been investigated.