  The promise of enhanced performance has motivated the study of one
dimensional nanomaterials, especially aligned carbon nanotubes (A-CNTs), for
the reinforcement of polymeric materials. While early work has shown that CNTs
have remarkable theoretical properties, more recent work on aligned CNT polymer
matrix nanocomposites (A-PNCs) have reported mechanical properties that are
orders of magnitude lower than those predicted by rule of mixtures. This large
difference primarily originates from the morphology of the CNTs that reinforce
the A-PNCs, which have significant local curvature commonly referred to as
waviness, but are commonly modeled using the oversimplified straight column
geometry. Here we used a simulation framework capable of analyzing 10$^{5}$
wavy CNTs with realistic stochastic morphologies to study the influence of
waviness on the compliance contribution of wavy A-CNTs to the effective elastic
modulus of A-PNCs, and show that waviness is responsible for the orders of
magnitude \textit{over-prediction} of the A-PNC effective modulus by existing
theoretical frameworks that both neglect the shear deformation mechanism and do
not properly account for the CNT morphpology. Additional work to quantify the
morphology of A-PNCs in three dimensions and simulate their full elastic
constitutive relations is planned.
