基于变分原理的机织复合材料细观力学模型

【作者】 魏广恒；

【导师】 黄故；

【作者基本信息】 天津工业大学 ， 纺织工程， 2006， 硕士

【摘要】 纺织复合材料本身具有明显的结构特性，是一种多相体材料。其力学性能及损伤破坏机理不仅取决于各组分材料的性能，同时也取决于细观结构特征。采用细观力学分析建立材料宏观力学性能与材料各组分性能以及细观结构参数之间的内在联系是材料科学发展的新趋势。本课题较系统地阐述了一般机织复合材料的细观结构划分，以及机织复合材料细观结构的参数表征方法，并建立了一般机织复合材料的细观结构模型。在此基础上，首次引入有限元约束变分原理和拉格朗日乘子法，建立了一个概念清晰、结果准确、通用性强的机织复合材料细观分析模型，该模型可用于有效预测机织复合材料在多向受载情况下的局部应力。该模型考虑了织物几何参数，纱线相互作用以及基体分布等因素。第一步，通过从上到下逐层分解的方法，将机织复合材料单胞从几何上分解成基体和纱线胞元；第二步，按照从下到上的均匀化方法，建立材料外部载荷和内部应力之间的联系。模型的关键在于使用拉格朗日乘子法来计算“应力集中因子”。最后，借助“应力集中因子”求出复合材料的三维刚度矩阵，进而可以求出实验材料的弹性常数。通过将材料的预测弹性常数与试验测出的弹性性能进行对比，验证了该预测模型的准确性。更多还原

【Abstract】 As a multiphase material, woven fabric composites have a significant structural mechanism. The mechanical behavior and failure mechanism of woven fabric composites depend significantly on its micro-structure and the properties of each constituent. It is a new trend to study the relationship between the macro-mechanical behavior and the properties of the constituents as well as the micro-structural parameters. In this paper, the general rules are illustrated to characterize the micro-structure of woven composites by some design parameters. A geometrical structure model of general woven composites is put forward. Based on the above studies, a simple variational principle and a method of Lagrangian multipliers are introduced for the first time to construct the mesomechanic model. Then a new mesomechanic model is presented to predict the mechanical properties of woven composites. The model accounts for fabric geometry, yarn interactions and yarn crisp. First, by constructing a multi-level decomposition scheme, the composites unit cell is split up into matrix and yarn cells. Then, by a multi-step homogenization procedure, a link is established between the external loading and the internal stresses. The principle idea lies in the interpretation that the "stress concentration factors" can be computed at each step by applying the complementary variational principle. In addition to modeling the stress and strain fields, the compliance matrix is computed in this paper using "stress concentration factors". Samples of woven preform and composites are made in the laboratory. At the end, the theoretical predictions of numerical stiffness are compared with the testing results and a good agreement is reported.更多还原