基于周期性边界条件的机织复合材料多尺度分析

Multi-Scale Analyses of Woven Composite Based on Periodical Boundary Condition

针对平纹机织复合材料,首先从微观纤维直径尺度,采用三维实体有限元方法计算纤维束的等效性能参数。然后将这些参数代入细观尺度的机织单胞模型中,得到宏观结构的平均弹性常数。在两个尺度有限元的分析中,均摒弃了传统有限元分析中采用的等应力或等应变假设,引入周期性边界条件,同时保证了周期性单胞边界面的应力连续和位移连续。分析结果表明,对于机织周期性单胞,在剪切和拉伸情况下其边界面均不全部保持为平面,纠正了此前认为在拉伸情况下单胞边界面仍保持平面的错误假设。纤维束分析结果与使用实验修正参数的细观力学理论公式结果吻合良好,织物单胞的分析结果也与弯曲层板组合模型结果较为接近,证明了分析方法的正确性。

Periodical representative volume elements （RVEs） are applied on two length scales to compute macroscopic stiffness characteristics of woven composites. On the smallest scale, the effective transversely isotropic properties of yarns are computed. The effective yarn properties are incorporated into a full woven RVE and effective stiffness properties of the woven composite are obtained. The periodical boundary conditions are applied to the two-scale FEM analyses to ensure stress continuous and strain continuous on boundary surfaces. Results demonstrate that surfaces of woven RVEs no longer keep as the plane after deformation both under shear and tensile loading cases. Thus, the assumption of the homogenous strain or the homogenous stress cannot be used in these cases. Results of yarns are in good agreement with the micro-mechanical one modified by experimental data. Properties of the woven composite agree well with data obtained from the bending layer model. Numerical data verify the correctness of the model and the method.