复合材料粘弹性性能预测的多尺度算法与数值模拟

【作者】 常崇义；

【导师】 刘书田；

【作者基本信息】 大连理工大学 ， 工程力学， 2003， 硕士

【摘要】 粘弹性是材料的重要性质。随着复合材料在工程中的广泛应用，尤其是复合材料在极端情况下(高温、高压、高速)，蠕变现象和松弛现象使得结构无法正常工作，这使复合材料的粘弹性性能的研究受到越来越多的重视。复合材料的宏观粘弹性性能取决于材料的微观结构和组分材料性质，通过调整微观结构和组分材料性质，可以改变材料的宏观粘弹性性能。因此，根据实际需要有目的地设计材料的微观结构，以使材料具有特定宏观粘弹性性能。这对指导复合材料的生产实践具有重要意义。因此，需要研究微观结构与宏观结构之间的关系，研究复合材料粘弹性性能预测的理论和方法。该方面的研究对于复合材料的微观设计和节省实验费用都具有重要意义。 本文利用多尺度均匀化理论研究层状复合材料、单向纤维增强复合材料的粘弹性本构关系及其与夹杂体积份数的变化规律，具体开展了下列有理论和应用价值的研究工作。 1、在阅读大量相关文献的基础上，介绍了复合材料性能和应用技术研究的重要意义和工程背景，综述了复合材料力学的研究进展，其中重点介绍了各种复合材料细观力学的发展情况。(详见第一章) 2、在简要介绍细观多尺度均匀化方法的基本理论的基础上，通过复合材料粘弹性问题的控制方程的Laplace变换，并利用对应原理，在像空间中导出了利用均匀化理论预测宏观松弛模量的Laplace变换泛函形式。(详见第二章) 3、建立了基于多尺度均匀化理论的层状复合材料粘弹性性能预测的基本方法及其与体分比的变化规律。首先对层状复合材料粘弹性问题的控制方程进行Laplace变换，在像空间中利用均匀化理论建立宏观松弛模量的Laplace变化与各层形式的依赖关系解析表达式，通过Laplace逆变换可获得等效松弛模量预测的解析表达式，并给出了体积变形为弹性、剪切变形符合三元件模型的单向节理岩石的粘弹性松弛模量预测的数值算例。在此基础上，用类似粘弹性三元件固体模型的形式去拟合离散的数值结果，得到了松弛模量更简单的解析表达式。(详见第三章) 4、建立了基于多尺度均匀化理论的单向纤维增强复合材料粘弹性性能预测的基本方法及其与夹杂体积份数的变化规律。首先对单向纤维增强复合材料粘弹性问题的控制方程进行Laplace变换，在像空间s中利用均匀化理论建立宏观松弛模量的Laplace变换泛函形式，根据粘弹性-弹性对应原理，用均匀化问题的有限元方法预报单向纤维增强复合材料在相空间中多个离散点的本构关系，然后根据典型粘弹性材料的松弛模量具有的函数形式进行曲线拟合，再通过对拟合出的函数进行Laplace逆变换，从而再回到时间t域，就得到了单向纤维增强复合材料的松弛模量。该方法利用合理的曲线拟合函数避开了复杂的数值Laplace逆变换，使得单向纤维增强复合材料的粘弹性性能的确定变得容易。给出的单向纤维复合材料的粘弹性松弛模量预测的数值算例验证了该方法的有效性。(详见第四章) 本文的研究工作得到国家自然科学基金(10072016)资助项目、教育部骨干教师资助计划、西安交通大学结构强度与振动国家重点实验室开放研究基金资助。更多还原

【Abstract】 Composite materials often exhibit viscoelastic behavior. The creep and relaxation of composite materials may lead the structures losing their function. The wide applications of composite structures make the research of the composite material’s viscoelastic properties become an important task. Recently, this research has attracted many attentions. The effective relaxation moduli of composites are dependent on the microstructure and viscoelastic properties of components of composite materials. Thus, materials with specific viscoelastic properties can be obtained by designing the microstructure and selecting the components of composite materials. A key problem is to determine the relationship of the macroscopic viscoelastic properties with the microstructure of the materials. In this thesis, homogenization-based methods for predicting the viscoelastic property of multi-layered composite materials and unidirectional fiber reinforced composite materials are presented, and the relation curves of the moduli of materials with and inclusion volume fraction are given in the article. The contents and the results of this research include:1. The engineering background and the importance of composition material research are presented. A review of the research developments in composite mechanics is given. And then the brief description of the researches in micro- mechanics is presented. (See Chapter 1)2. The basic conception of the homogenization theory is given, and then by Laplace transforming, the formulae for predicting the viscoelastic relaxation moduli in Laplace transformed domain are obtained from the governing equation of the problem of composite materials. (See Chapter 2)3. A homogenization-based method for predicting the viscoelastic property of multi-layered composite material is presented. By Laplace transforming the governing equation of the viscoellastic problem of jointed rock, the dependent relation of the Laplace transformation of the effective relaxation modulus of jointed rock on the joint distribution was derived by applying the homogenization method in Laplace transformed domain. Then, the effective relaxation modulus was obtained from the inverse transformation. Numerical example was presented. On base of those, effective relaxation moduli could be curve-fitted by the function form of the three-parameter solid model. The simpler explicit formulae for the prediction of the viscoelasticity property are obtained. (See Chapter 3)4. A homogenization-based method for predicting the viscoelastic property of unidirectional fiber reinforced composite materials is presented. By Laplace transforming the governing equation of the problem of unidirectional fiber reinforced composite materials, the formulae for predicting the viscoelastic relaxation moduli in Laplace transformed domain are obtained. According to correspondence principle of viscoellastic mechanics and elastic, mechanics, the results of effective moduli for several s are obtained by using the finite element method of the homogenization. Then effective relaxation moduli should be curve-fitted, according to the viscoelastic relaxation modulus formulae of many viscoelastic materials. The viscoelastic relaxation moduli in time domain are obtained by the inverse Laplace transform of the curve-fitted formulae. The method takes advantage of rational curve-fitted formulae and avoids complicated numerical inverse Laplace transform. That makes the prediction of viscoelastic relaxation moduli easy. The numerical example was presented in the end of this paper. (See Chapter 4)The work of this thesis is supported by National Nature Science Foundation of China (No. 10072016), and by Special Founding for University Key Teachers of Education Ministry of China and the Open Research Fund of the State Key Lab of Structure strength and Vibration, Xi’an Jiaotong University.更多还原