Numerical homogenization of N-component composites including stochastic interface defects

The purpose of this paper is to present a mathematical formulation and numerical analysis for a homogenization problem of random elastic composites with stochastic interface defects. The homogenization of composites so de"ned is carried out in two steps: (i) probabilistic averaging of stochastic discontinuities in the interphase region, (ii) probabilistic homogenization by extending the e!ective modules method to media random in the micro-scale. To obtain such an approach the classical mathematical homogenization method is formulated for n-component composite with random elastic components and implemented in the FEMbased computer program. The article contains also numerous computational experiments illustrating stochastic sensitivity of the model to interface defects parameters and verifying statistical convergence of probabilistic simulation procedure