Modeling of Fracture Behavior in Polymer Composite Using Concurrent Multi-Scale Coupling Approach

Abstract

Embedded statistical coupling method (ESCM) was developed to provide computational efficiency, to decrease coupling complexities, and to avoid discretization of the continuum model to atomic scale resolution in concurrent multi-scale modeling. ESCM scheme is relatively easy to implement with conventional FEM code and has been tested in standard solid lattice structures. However, this method encounters difficulties when being implemented into amorphous materials like polymers, due to the fact that they lack specific ordered lattice structure and atoms may not be covalently bonded with each other, which are the requirements of common coupling schemes. Therefore, a new approach needs to be developed to solve this problem. In this work, details of a modified ESCM approach for atomistic-continuum coupling developed to perform simulations of crack growth in polymers is presented. The presence of the continuum domain surrounding the MD region prevents stress wave reflections from the external boundary impinging back on the crack tip. In this approach, generalized interpolation material point method (GIMP), which is a meshless particle-in-cell method based on Arbitrary Euler-Lagrange (ALE) scheme and has been proven to have good performance in large deformation problems, is used as the continuum domain. It is concurrently coupled with molecular dynamics (MD), a widely used method in atomistic simulations, using a so-called handshake region. Anchor points, the equilibrium positions of the constrained particles, which are designed to transmit displacements and forces between nanoscale and macroscale model, are defined in the handshake region. A concurrently coupled GIMP-MD simulation of nanoscale crack propagation inside a polymer is performed to verify this new coupling approach, and provide a better understanding of the fracture mechanisms at nanoscale to predict the macro-scale fracture toughness of polymer system. Results are presented for concurrently coupled crack propagation in a di-functional cross-linked thermoset polymer, EPON 862.