2-D nano-scale finite element analysis of a polymer field

Abstract

Two types of 2-D nano-scale finite elements, the chemical bond element and the Lennard–Jones element, are formulated based upon inter-atomic and inter-molecular force fields. A nano-scale finite element method is employed to simulate polymer field deformation. This numerical procedure includes three steps. First, a polymer field is created by an off-lattice random walk, followed by a force relaxation process. Then, a finite element mesh is generated for the polymer field. Chemical bonds are modeled by chemical bond elements. If the distance between two non-bonded atoms or monomers is shorter than the action range of the Lennard–Jones attraction (or repulsion), a Lennard–Jones element is inserted between them. Finally, external load and boundary conditions are applied and polymer chain deformation is simulated step by step. During polymer deformation, failed Lennard–Jones bond elements are removed and newly formed Lennard–Jones elements are inserted into the polymer field during each loading step. The process continues until failure occurs. Two examples are presented to demonstrate the process. Stress–strain curves of polymer fields under unidirectional tensile load are derived. Continuum mechanical properties, such as modulus and polymer strength, are determined based upon the stress strain curve. Further, throughout the deformation process one observes polymer chain migration, nano-scale void generation, void coalescence and crack development.