S. Qu, V. Shastry, W. A. Curtin and R. E. Miller
Modelling and Simulation in Materials Science and Engineering, 13, 1101–1118 (2005).
A method for simultaneously thermostatting an atomistic region and absorbing energetic pulses impinging on the atormstic/continuum interface from the atomistic region is developed to operate within the framework of the coupled atomistic/discrete dislocation method. The approach inserts an additional Langevin damping term and a random force term into the equations of motion for atoms in a 'stadium' boundary region near the atom/continuum interface, with the damping coefficient ramped linearly over the width of the region, as suggested by Holian and Ravelo. The remaining interior atom dynamics are computed using a standard MD algorithm with no artificial damping or thermostatting. The continuum region deformations are computed using static FEM updated stochastically over time scales comparable to the Debye frequency of the atoms using time-averaged displacements at the atom/continuum interface, thereby providing an evolution of the continuum region that tracks the atomistic deformation. The method is evaluated by studying the ability of the coupled system: (i) to equilibrate the inner atomistic region at a desired temperature under conditions of no external or internal loading, (ii) to produce the proper canonical thermal fluctuations and (iii) to absorb deformation pulses initiated in the interior region and incident upon the atomistic/continuum boundary. With an optimal maximum damping coefficient of approximately 1/2 of the Debye frequency, temperature stability is attained at values very close to the target temperature. The temperature variance agrees well with the canonical expectation for various temperatures. For the same damping parameters and at low temperature, high-energy deformation pulses propagate unimpeded up to the stadium boundary region and then are completely damped out upon approach to the atomistic/continuum interface with no measurable reflections. At higher temperatures, thermal fluctuations in the total energy make analyses difficult, but damping of high-energy deformation pulses is achieved within the limits of the thermal noise in the system while observation of the time-dependent displacements shows no observable reflections.