Modeling and analysis of interphase damage in carbon nanotube reinforced materials and structures

该项目的主要目标是将当前项目中考虑的随机碳纳米管增强材料（CNTRM）的线性建模能力扩展到非线性、非弹性范围。第二个目标是证明所提出的方法在其应用中的有效性，在复合材料结构元素的应力和应变场的分析。更具体地说，目标是开发一种方法来评估与基体/非均匀界面损伤相关的CNTRM的整体非线性行为。要特别强调CNT的有限纵横比和它们的随机排列。为了实现上述目标，能量等效不均匀性（EEI）的方法随机材料的界面，在当前的项目中开发，将被采用。它将与PI早先提出的用于分析无界面复合材料的3D统计损伤模型的2D版本相结合。2D界面的损伤将根据界面应变和应力的统计平均值来制定，其评估由当前项目中设计的EEI方法实现。这种能力将当前项目与拟议的研究联系起来。因此，EEI为基础的均匀化方法提出的线性问题与界面的当前项目将直接适用于非线性问题，除了在非线性分析的属性界面将不会是恒定的，但会演变的推进损伤。考虑材料的随机结构，对界面损伤及其演化的描述将是统计的，对于任意给定的加载历史，迭代过程将导致特定随机复合材料的非线性应力-应变关系，这是非线性问题所必需的。它将被应用到CNTRM的分析，并将通过与文献中的实验结果进行比较来验证。所提出的方法的实际好处和潜力将被证明由代表性的复合材料结构的几何形状和加载的有限元分析是感兴趣的应用。

The main goal of the project is the extension of linear modeling capabilities of random Carbon NanoTube Reinforced Materials (CNTRM), considered in the current project, into a nonlinear, inelastic range. The secondary goal is to demonstrate the effectiveness of proposed approach in its application to analysis of stress and strain fields in composite structural elements.More specifically, the goal is to develop a method of evaluating the overall nonlinear behavior of CNTRMs associated with damage of matrix/inhomogeneity interphases. The finite aspect ratio of CNTs and their random arrangement is to be particularly emphasized. To achieve the above goals, the Energy Equivalent Inhomogeneity (EEI) approach to random materials with interphases, developed in the current project, will be employed. It will be combined with the 2D version of the 3D statistical damage model for analysis of composites without interphases, proposed earlier by the PI. Damage of 2D interphases will be formulated in terms of the statistical averages of the interphase strains and stresses, evaluation of which is enabled by the EEI approach devised in the current project. This ability crucially links the current project with the proposed research. As a result, the EEI-based homogenization approach proposed in the current project for linear problems with interphases will be directly applicable to nonlinear problems, except that in nonlinear analysis the properties of the interphases will not be constant but will evolve in view of the advancing damage. Given the random structure of the considered materials, the proposed description of the interphase damage, and of its evolution, will be statistical.The iterative process, necessitated by the nonlinearity of the problem, which for any prescribed loading history will lead to the nonlinear stress-strain relationship for a specific random composite, will be developed. It will be applied to analysis of CNTRM and will be verified by comparison with experimental results available in the literature. The practical benefits and the potentials of the proposed approach will be demonstrated by the finite element analysis of representative composite structures whose geometry and loading is of interest in applications.