Fiber waviness in nanotube-reinforced polymer composites—II: modeling via numerical approximation of the dilute strain concentration tensor

Nanotube-reinforced polymers offer significant potential improvements over the pure polymer with regard to mechanical, electrical and thermal properties. This article investigates the degree to which the characteristic waviness of nanotubes embedded in polymers can impact the effective stiffness of these materials. A 3D finite element model of a single infinitely long sinusoidal fiber within an infinite matrix is used to numerically compute the dilute strain concentration tensor. A Mori–Tanaka model utilizes this tensor to predict the effective modulus of the material with aligned or randomly oriented inclusions. This hybrid finite elementmicromechanical modeling technique is a powerful extension of general micromechanics modeling and can be applied to any composite microstructure containing non-ellipsoidal inclusions. The results demonstrate that nanotube waviness results in a reduction of the effective modulus of the composite relative to straight nanotube reinforcement. The degree of reduction is dependent on the ratio of the sinusoidal wavelength to the nanotube diameter. As this wavelength ratio increases, the effective stiffness of a composite with randomly oriented wavy nanotubes converges to the result obtained with straight nanotube inclusions. The approach developed in this paper can also be utilized in the analysis of other problems involving nanotube-reinforced polymers, including alternate nanotube representations, viscoelastic response, assessing the effect of low matrix-NT bond strength and in the determination of thermal and electrical conductivity. # 2003 Elsevier Ltd. All rights reserved.