Coupled effect of CNT waviness and agglomeration: A case study of vibrational analysis of CNT/polymer skew plates

The main contribution of this work lies in a critical comparison of different mean-field homogenization approaches for the study of carbon nanotube-reinforced polymers with waviness and agglomeration effects. In particular, this paper focuses on the consistency of predictions in terms of diagonal symmetry of the constitutive tensors and comparison against theoretical bounds. The analysis comprises general axisymmetric orientation distributions of fillers, both planar sinusoidal and helical wavy fillers, as well as different agglomeration schemes by means of a two-parameter agglomeration model. The results demonstrate that waviness and agglomeration simultaneously weaken the macroscopic stiffness of composites. The results also reveal that the widely used Mori-Tanaka method fails to simulate the coupled effect of these two phenomena and, therefore, it is necessary to apply extended approaches with consideration of ad hoc Eshelby's tensors that account for particular wavy microstructures. A case study of carbon nanotube-reinforced skew plates is finally presented to illustrate the coupled effect of waviness and agglomeration on the macroscopic vibrational behavior.