Stochastic contact effects in periodic fibre composites

In this paper stochastic contact effects in the field of structural computational mechanics are introduced. The main ideas of this formulation are:

1. Approximation of unknown stochastic geometry of the contact surface by a sequence of assumed figures; volume and frequency of occurring on considered surface are Gaussian random variables with specified statistics

2. Replacing random contact region including all these figures with stochastically averaged material occupying deterministic contact region

3. Numerical solution to the stochastic static problem formulated in this way using the Stochastic Finite Element Method (SFEM).

Proposed model is intended for analysis of interface discontinuities in periodic fibre composites with random elastic properties, however there are many more complicated problems in which the presented method can be employed with a good result. In numerical analysis a quarter of square periodicity cell with round, centrally placed fibre is analysed using POLSAP and ABAQUS systems.