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

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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.