Numerical homogenization ofN-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 defined is carried out in two steps: (i) probabilistic averaging of stochastic discontinuities in the interphase region, (ii) probabilistic homogenization by extending the effective 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 FEM-based 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.