Effect of matrix constraint and boundary conditions on the buckling behavior of carbon nanotubes in polyethylene

Molecular dynamics simulations were performed to investigate the buckling behavior of triple-walled carbon nanotubes (TWCNTs) embedded in a polyethylene (PE) matrix under uniaxial compression. To clarify the effects of the surrounding matrix and boundary constraints, pure TWCNT models were compared with periodic boundary condition (PBC) models having three transverse dimensions (small, medium, and large) and a fixed-wall (FW) model providing rigid lateral constraints. The TWCNTs buckled by two competing modes. Local (shell-wall) buckling was governed by a critical local compressive stress of approximately 46 GPa for the nanotube studied here, while global (Euler-type) bending followed continuum column theory for longer, bare nanotubes. For short tubes ( ≤ 20 nm), matrix-induced stress non-uniformity drove the local stress to a buckling threshold at a lower average stress, reducing the buckling stress from 44.0 GPa for pure TWCNTs to approximately 35–38 GPa. Longer pure TWCNTs buckled globally with S-shaped bending; the surrounding PE suppressed this bending via shear resistance and raised the buckling stress. The stabilization scaled with the transverse matrix area once the matrix was thick enough to act as a surrounding medium rather than an interfacial layer. Under strong lateral constraints, as in the FW model, the failure mode was local buckling, resulting in a length-independent buckling strength in the range of 33–38 GPa. These results indicate that the matrix lowered the threshold for local buckling via stress non-uniformity, while simultaneously stabilizing long TWCNTs against global bending. Observed failure modes reflected the balance between these two competing effects.