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A Finite Element Model for Estimating Young-s Modulus of Carbon Nanotube Reinforced Composites Incorporating Elastic Cross-Links

The presence of chemical bonding between functionalized carbon nanotubes and matrix in carbon nanotube reinforced composites is modeled by elastic beam elements representing covalent bonding characteristics. Neglecting other reinforcing mechanisms in the composite such as relatively weak interatomic Van der Waals forces, this model shows close results to the Rule of Mixtures model's prediction for effective Young's modulus of a Representative Volume Element of composite for small volume fractions (~1%) and high aspect ratios (L/D>200) of CNTs. Keywords—Beam Element, Carbon Nanotube Reinforced Composite, Cross-link, Young's modulus. I. INTRODUCTION ARBON Nanotubes (CNTs) have attracted researchers' great attention due to their outstanding mechanical, electrical, thermal, chemical, and even biological properties. Young's modulus, strength, strain before failure, and aspect ratio in CNTs are significantly high which bring about application of CNTs as composites reinforcement, and thus providing versatile characteristics for composites. The small size of nanostructure of such composites brings sever limitations in conducting experimental studies, thus encouraging scientists to develop theoretical models in order to explore their mechanical behavior. CNT reinforced composites have been investigated by multiscale modeling bridging the length scales from nano- through the mesoscale (1-3). Description of the interaction between the CNT (reinforcement) and the matrix is of great importance in analysis of CNT reinforced composites, as several models