Modeling of fracture behavior in polymer composites using concurrent multi-scale coupling approach

SB Li and S Roy and V Unnikrishnan, MECHANICS OF ADVANCED MATERIALS AND STRUCTURES, 25, 1342-1350 (2018).

DOI: 10.1080/15376494.2016.1227510

Embedded statistical coupling method was originally developed to provide computational efficiency, to decrease coupling complexities, and to avoid the need to discretize the continuum model to atomic scale resolution in concurrent multi-scale modeling. An embedded statistical coupling method scheme is relatively easy to implement within a conventional finite element method code and has been tested in standard solid lattice structures. However, this method encounters difficulties when being implemented for 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 resolve this problem. In this article, details of a modified embedded statistical coupling method approach for atomistic-continuum coupling developed to perform simulations of macroscale crack growth in polymers is presented. The presence of the continuum domain surrounding the molecular dynamics region allows for the application of far field loading, and prevents stress wave reflections from the external boundary impinging back on the crack tip. In our approach, a material point method, which is a meshless particle-in-cell method based on an arbitrary Euler-Lagrange scheme and has been proven to have good performance in large deformation problems, is used to model the continuum domain. It is concurrently coupled with molecular dynamics, 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 material point method-molecular dynamics simulation of crack propagation inside a polymer is performed to verify this new coupling approach, thereby providing a better understanding of the fracture mechanisms at the nanoscale to predict the macro-scale fracture toughness of a polymer system. Results are presented for concurrently coupled simulation of crack initiation and crack propagation in a di-functional cross-linked thermoset polymer, EPON 862.

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