Determination of the representative volume element model critical size for carbon fiber reinforced polymer composites

The critical size is a prerequisite to accurately evaluate mechanical properties by utilizing the representative volume element (RVE) model. This study proposes a method to determine the RVE model critical size based on statistical theory. First of all, the distribution types followed by the calculated results of models are tested by hypothesis test methods. Afterwards, the least sample for a given confidence level is determined by using the t-test. Lastly, the RVE model critical size is determined by analyzing the dispersion of statistics. The results show that the mechanical properties of different models for the same size follow a normal distribution. The least sample exists where the error of mechanical properties is stable. By quantifying the dispersion of mechanical properties, the RVE model critical size is determined at low significance level and low critical error, hence the error of results for an arbitrary model with this size can be quantified.

Automated summary

This study proposes a method to determine the critical size of the RVE model based on statistical theory. It tests the distribution types of the models using hypothesis test methods and determines the least sample for a given confidence level using the t-test. The critical size of the RVE model is determined by analyzing the dispersion of statistics. The results show that the mechanical properties of different models for the same size follow a normal distribution, and the least sample exists where the error of mechanical properties is stable. By quantifying the dispersion of mechanical properties, the critical size of the RVE model can be determined, allowing for quantification of the error of results for an arbitrary model with this size.