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.

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

Artioli E.;Beirao da Veiga L.;Verani M.
2020

Abstract

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.
A posteriori error estimate
Asymptotic homogenization
Curved edges
Random composite
Virtual element method
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1142902
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