Peridynamic Modeling and Simulation of Polymer-Nanotube Composites

In this document, we develop and demonstrate a framework for simulating the mechanics of polymer materials that are reinforced by carbon nanotubes. Our model utilizes peridynamic theory to describe the mechanical response of the polymer and polymer-nanotube interfaces. We benefit from the continuum formulation used in peridynamics because (1) it allows the polymer material to be coarse-grained to the scale of the reinforcing nanofibers, and (2) failure via nanotube pull-out and matrix tearing are possible based on energetic considerations alone (i.e. without special treatment). To reduce the degrees of freedom that must be simulated, the reinforcement effect of the nanotubes is represented by a mesoscale bead-spring model. This approach permits the arbitrary placement of reinforcement ''strands'' in the problem domain and motivates the need for irregular quadrature point distributions, which have not yet been explored in the peridynamic setting. We address this matter in detail and report on aspects of mesh sensitivity that we uncovered in peridynamic simulations. Using a manufactured solution, we study the effects of quadrature point placement on the accuracy of the solution scheme in one and two dimensions. We demonstrate that square grids and the generator points of a centroidal Voronoi tessellation (CVT) support solutions of similar accuracy, but CVT grids have desirable characteristics that may justify the additional computational cost required for their construction. Impact simulations provide evidence that CVT grids support fracture patterns that resemble those obtained on higher resolution cubic Cartesian grids with a reduced computational burden. With the efficacy of irregular meshing schemes established, we exercise our model by dynamically stretching a cylindrical specimen composed of the polymer-nanotube composite. We vary the number of reinforcements, alignment of the filler, and the properties of the polymer-nanotube interface. Our results suggest that enhanced reinforcement requires an interfacial stiffness that exceeds that of the neat polymer. We confirm that the reinforcement is most effective when a nanofiber is aligned with the applied deformation, least effective when a nanofiber is aligned transverse to the applied deformation, and achieves intermediate values for other orientations. Sample configurations containing two fibers are also investigated.