Probabilistic homogenization of hexagonal honeycombs with perturbed microstructure
The present study is concerned with a numerical determination of the effective mechanical properties of hexagonal honeycombs with irregular random cell geometry. Based on a regular hexagonal model, a perturbation technique is employed for generation of randomized microstructures by repositioning of the cell wall intersections within prescribed areas. Using a large number of numerical experiments, the entire set of testing volume elements is statistically representative for the random microstructure of the honeycomb material. Subsequently, the effective mechanical properties of the microstructural model are determined by means of a strain energy based homogenization procedure. Both the effective stiffness and the effective strength are examined. The stochastic information about the scatter in the effective properties is gained from repeated numerical experiments on small scale testing volume elements for the microstructure. Compared to a single analysis of a large scale, statistically representative volume element, the repeated analysis of small scale testing volume elements proves to be rather efficient. Furthermore, the statistical distributions of the effective properties can be determined in addition to their mean values.