An atomistic-continuum concurrent statistical coupling technique for amorphous materials using anchor points

A generalized framework for anchor point based concurrent coupling of finite element method (FEM) and molecular dynamics (MD) domains, incorporating previous related methods, is presented. The framework is robust and is agnostic of material crystallinity and atomistic description. The method follows an iterative approach to minimize the total energy of the coupled FEM-MD system, while maintaining displacement constraints between the domains. Two distinct forms of the coupling method are discussed in detail, differing in the nature of the constraint, both of which are able to make use of specialized MD solvers such as LAMMPS with little or no modification. Both methods make use of springs that join groups of atoms in the MD to the FEM domain. Method 1, termed 'Direct Coupling', couples MD anchor points directly to the FEM domain in a force-based manner and has the added advantage of being able to couple to specialized FEM solvers such as ABAQUS. Method 2 couples the MD to the FEM domain in a more 'soft' manner using the method of Lagrange multipliers and least squares approximation. The relative performance of these two methods are tested against each other in a uniaxial tension test using a graphene monolayer at 300 K temperature and a block of thermosetting polymer EPON862 at low temperature, showing comparable results. Convergence behaviour of the two coupling methods are studied and presented. The methods are then applied to the fracture of a centre-cracked graphene monolayer and compared with results from an identical pure MD simulation. The results corroborate the effectiveness of the developed method and potential use as a plug-and-play tool to couple pre-existing specialized FEM and MD solvers. Future work will focus on applying these methods to simulate elevated-temperature amorphous polymer models and their brittle fracture.