A Concurrent Multi-Scale Method for Coupling Atomistic and Continuum Models at Finite Temperatures
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1229-LL04-07
A Concurrent Multi-Scale Method for Coupling Atomistic and Continuum Models at Finite Temperatures R.C. Picu and N. Mathew Department of Mechanical, Aerospace and Nuclear Engineering and Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. ABSTRACT A concurrent multi-scale modeling method for finite temperature simulation of solids is introduced. The objective is to represent far from equilibrium phenomena using an atomistic model and near equilibrium phenomena using a continuum model, the domain being partitioned in discrete and continuum regions, respectively. An interface sub-domain is defined between the two regions to provide proper coupling between the discrete and continuum models. While in the discrete region the thermal and mechanical processes are intrinsically coupled, in the continuum region they are treated separately. The interface region partitions the energy transferred from the discrete to the continuum into mechanical and thermal components by splitting the phonon spectrum into “low” and “high” frequency ranges. This is achieved by using the generalized Langevin equation as the equation of motion for atoms in the interface region. The threshold frequency is selected such to minimize energy transfer between the mechanical and thermal components. Mechanical coupling is performed by requiring the continuum degrees of freedom (nodes) to follow the averaged motion of the atoms. Thermal coupling is ensured by imposing a flux input to the atomistic region and using a temperature boundary condition for continuum. This makes possible a thermodynamically consistent, bi-directional coupling of the two models. INTRODUCTION There has been much interest in the scientific community for developing multi-scale methods that combine various material models in given problem representation. These models may represent the same physics with different spatial and temporal resolution and may be amenable to computational implementations that require dramatically different resources. Typically, models providing a more detailed description of the physics are also more computationally demanding. In regions of the problem domain in which accuracy on all scales is not critical, as for example in regions where field gradients are small, models providing a coarser (e.g. homogenized) description may be used. Coupling discrete and continuum representations of matter within the same problem domain is an extreme example of such attempt. Discrete representations are usually of atomistic type and require the explicit consideration of all atoms. The quantities of interest, such as displacements and stresses, are defined point wise, the inter-particle interactions are described by inter-atomic potentials and Newton’s equations of motion are used to represent dynamics. Continuum representations operate with fields and use differential forms of the conservation laws. The constitutive information is provided by material-dependent relations between field quantities. In this report we pre
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