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.

中文翻译：

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一种用于随机纤维增强复合材料统计均匀化的自适应弯曲虚拟元方法

摘要 我们提出了一种自适应弯曲虚拟元方法 (ACVEM)，该方法能够通过稳健且有效的基于残差的后验误差估计器将所涉及的计算几何的精确表示和最佳网格分辨率的动态调整相结合。对估计器可靠性的理论分析和一系列数值测试支持所提出方法的有效性。ACVEM 与蒙特卡罗模拟相结合，并开发了一种方法来确定在反平面剪切变形框架内随机长纤维增强复合材料的均质材料模量和代表性晶胞尺寸。所提出的均质化程序的准确性和计算效率通过数值例子得到证实。