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Carbon nanotubes (CNT)-reinforced polymer composite has many engineering applications due to attractive properties, like high strength to weight ratio. These materials are subjected to cyclic fatigue loading during their service life. This work proposed a dual scale modeling approach to predict fatigue crack growth behavior of CNT-reinforced polymer composite under the thermo-mechanical loading environment. The effective orthotropic property of CNT-reinforced polymer composite is estimated using the mean-field homogenization technique in meso-scale modeling. Further, the equivalent composite property is used for macro-scale fatigue crack growth study using higher-order extended finite element method. To present the efficiency of the proposed modeling approach, various combinations of polymer composite (by volume fraction of reinforcement at 7.5%, 10%, 12.5%, 15%, 17.5%, and 20%) are taken for analysis. At macro-scale modeling, XFEM with higher-order enrichment terms is employed to improve the solution accuracy at the crack tip region. The proposed computational approach has been employed with the in-house developed MATLAB code and DIGIMAT software. Several numerical examples are considered with geometrical discontinuities like multiple holes and cracks.

In this paper, by introducing the appropriate conformal transformation and using the complex variable function method, the problem about an elliptic hole with III asymmetry cracks in one-dimensional hexagonal piezoelectric quasicrystals is sovlved and the SIFs at the crack tip are obtained in the case of impermeable and permeable boundary conditions. In some special onditions, the cracks can be turned into a Griffith crack. By imitation computation, we can get the SIFs at the tip of the Griffith crack. especially, when the quasicrystals become vestigial the crystal, we can also get the SIFs at the tip of the Griffith crack, which is in accordance with the know results.