An adaptive curved virtual element method for the statistical homogenization of random fibre-reinforced composites

We propose an adaptive curved virtual element method (ACVEM) which is able to combine an exact representation of the involved computational geometry and a dynamic tuning of the optimal mesh resolution through a robust and efficient residual-based a-posteriori error estimator. A theoretical analysis on the reliability of the estimator and a gallery of numerical tests supports the efficacy of the proposed approach. The ACVEM is combined with Monte Carlo simulations, and a methodology is developed to determine homogenized material moduli and representative unit cell size of random long-fibre reinforced composites in the framework of antiplane shear deformation. Accuracy and computational efficiency of the proposed homogenization procedure is confirmed by numerical examples.