Finite Temperature Multiscale Methods
Ron Miller (Carleton University)
Collaborators: W. A. Curtin, (Brown), Laurent Dupuy (LLNL),
Rob Phillips (CalTech), S. Qu, (Brown), B. Shiari (NRC, Canada), V. Shastry (Brown), Ellad Tadmor (Technion),

The Quasicontinuum (QC) method uses simultaneous simulation of atomistic and continuum (finite element) regions to allow significant reduction in the computational overhead for large atomistic systems. Originally developed as a zero temperature, equilibrium method, the QC has been used to study quasi-static deformation problems such as nano-indentation, fracture and grain boundary sliding.

Recently, we have developed a finite temperature formulation that puts the QC on a rigorous statistical mechanics footing. The model makes
use of the local harmonic approximation of LeSar et al (PRL 63:624
(1989)) to account for the entropy of the unrepresented atoms in the
continuum regions. The resulting formulation correctly captures the
thermal expansion and temperature-dependent elastic constants of the
underlying atomistic potentials. Using a Nose-Poincare thermostat to
maintain contact with a finite temperature heat bath, the model
permits equilibrium molecular dynamics simulations with a significant
reduction in the number of atoms needed to represent the system.

We have also recently developed two techniques for including
temperature effects in the coupled atomistic and discrete dislocation
(CADD) model of Shilkrot, Miller and Curtin. In this model, an atomistic region is coupled to a continuum region that can support dislocations as elastic defects. We investigate the efficacy of the so-called "stadium boundary conditions" of Holian and Ravelo to mitigate wave reflections from the atomistic/continuum interface and to moderate the temperature in the atomistic region. We find that it is necessary to include an additional Langevin damping term and a random force term to make the method reasonably accurate.

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