We propose a computational procedure to assess size effects in nonfunctionalized single-walled carbon nanotube (CNT)-polymer composites. The procedure upscales results obtained with atomistic simulations on a composite unit cell with one CNT to an equivalent continuum composite model with a large number of CNTs. Molecular dynamics simulations demonstrate the formation of an ordered layer of polymer matrix surrounding the nanotube. This layer, known as the interphase, plays a central role in the overall mechanical response of the composite. Due to poor load transfer from the matrix to the CNT, the reinforcement effect attributed to the CNT is negligible; hence the interphase is regarded as the only reinforcement phase in the composite. Consequently, the mechanical properties of the interface and the CNT are not derived since their contribution to the elastic response of the composite is negligible. To derive the elastic properties of the interphase, we employ an intermediate continuum micromechanical model consisting of only the polymer matrix and a three-dimensional fiber representing the interphase. The Young's modulus and Poisson's ratio of the equivalent fiber, and therefore of the interphase, are identified through an optimization procedure based on the comparison between results from atomistic simulations and those obtained from an isogeometric analysis of the intermediate micromechanical model. Finally, the embedded reinforcement method is employed to determine the macroscopic elastic properties of a representative volume element of a composite with various fiber volume fractions and distributions. We then investigate the role of the CNT diameter on the elastic response of a CNT-polymer composite; our simulations predict a size effect on the composite elastic properties, clearly related to the interphase volume fraction.

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The development of carbon nanotube(CNT)-polymer composites advocates for a better understanding of their physical and mechanical properties that depend on the diameter of the embedded CNTs. Given that the experimental assessment of size effects is extremely difficult, the use of numerical models can be enormously helpful. However, since size effects might be observed both at the nano- and the macroscale, an adequate multiscale procedure is required. In this thesis, numerical techniques are explored to develop a multiscale approach for the analysis of size effects in the elastic response of CNT-polymer composites. Atomistic simulations, such a molecular mechanics and molecular dynamics, are used for the characterization of the composites and their components at the nanoscale. The obtained results are then used to investigate size effects in the macroscopic properties of CNT-polymer composites using continuum models and efficient finite element techniques. Molecular mechanics simulations on tensile carbon nanotubes show that their axial stiffness and axial strain field depend on the CNT diameter. Moreover, it is found that the axial strain field can be accurately reproduced using nonlocal continuum models if optimal nonlocal parameters, that vary with the nanotube diameter, and a suitable nonlocal kernel are used. Although the numerical solution of nonlocal problems is typically challenging, higher order B-spline finite elements overcome the issues encountered when standard approximation techniques are employed. Further, molecular dynamics simulations on CNT-polymer composites show that the CNT diameter alters the atomic structure and the mechanical properties of the ordered layer of polymer chains forming around the nanotube —the interphase. Such a layer has a significant impact on the mechanical properties of the composite. Although the role of the nanotubes during elastic deformation of the composite is negligible due to the weak nonbonded interface interactions, the interphase–thanks to its highly ordered atomic structure–is shown to enhance its mechanical properties. Here, molecular mechanics simulations at the nanoscale and the numerical solution of an equivalent continuum model at the macroscale indicate that the composite stiffness increases when the diameter of the carbon nanotubes is decreased. When possible, the reliability of the results in this thesis has been assessed by means of analytical models and experimental or numerical results in the literature. Therefore, this study proposes a computational framework to improve our understanding of the mechanical response of CNT-polymer composites and the size effects on their elastic properties.@en

Molecular-dynamics simulations of single-walled carbon nanotubes (CNTs) embedded in a coarse-grained amorphous monodisperse polyethylene-like model system have been carried out. The roles of nanotube diameter and chirality on the physical and structural properties of the composite are thoroughly discussed for several CNTs with different diameter and chirality. It is shown that the glass-transition temperature of the polymer matrix increases with the diameter of the CNT while chirality effects are negligible. A denser and ordered layered region of polymer matrix is found in the vicinity of the nanotube surface. The density and ordering of this layer increases with the CNT diameter. All simulations indicate that chirality does not affect the atomic structure of the highly ordered layer surrounding the CNTs. Despite the simplicity of the polymer model, results of this study are qualitatively comparable with those obtained from experiments and numerical simulations that consider a chemically specific polymer matrix.

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