基于修正高精度广义胞元法的复合材料细观力学分析

高精度广义胞元法是多尺度分析复合材料模量和微观应力应变场的有效方法之一．然而，由于位移插值函数中缺少二次耦合项，很大程度上影响了复合材料局部应力、应变场，特别是剪切场的计算精度．本文通过引入二次方向耦合项，提出了一种修正的高精度广义胞元法插值函数．在施加周期性边界条件、平均应力和平均位移连续性条件后，可以确定位移插值函数中的系数．通过对多相复合材料弹性模量和局部场分析，并且与有限元分析和实验测量结果比较，验证了修正高精度广义胞元法的准确性．与高精度广义胞元相比，本文提出的修正高精度广义胞元法在不需要引入额外未知变量，不影响计算效率的前提下，对复合材料的局部应力场计算得更加准确．

Micromechanics Analysis of Composite Materials Based on the Modified High Fidelity Generalized Method of Cells

The High Fidelity Generalized Method of Cells(HFGMC) is a powerful technique for multiphase composite simulation. However, there are some disadvantages in the simulation accuracy for the local stress and strain fields due to the lack of quadratic coupling term in the interpolation functions. A modified HFGMC(M-HFGMC) is proposed by introducing the quadratic directional coupling term in the interpolation function. Based on the periodic boundary conditions, and the continuity conditions of averaged stress and displacement, the coefficients in the displacement expansions are determined. The mechanical properties and the local fields of the multiphase composite are well predicted, which is verified by the finite element method and the experiments, respectively. Compared with HFGMC theory, without any more variables, the M-HFGMC can provide more accurate prediction of the local stresses in the composites without sacrificing the computational efficiency due to introduction of additional variables.