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Multiscale modeling of the dynamics of solids at finite temperature. (English) Zbl 1120.74313

Summary: We develop a general multiscale method for coupling atomistic and continuum simulations using the framework of the heterogeneous multiscale method (HMM). Both the atomistic and the continuum models are formulated in the form of conservation laws of mass, momentum and energy. A macroscale solver, here the finite volume scheme, is used everywhere on a macrogrid; whenever necessary the macroscale fluxes are computed using the microscale model, which is in turn constrained by the local macrostate of the system, e.g. the deformation gradient tensor, the mean velocity and the local temperature. We discuss how these constraints can be imposed in the form of boundary conditions. When isolated defects are present, we develop an additional strategy for defect tracking. This method naturally decouples the atomistic time scales from the continuum time scale. Applications to shock propagation, thermal expansion, phase boundary and twin boundary dynamics are presented.

MSC:

74A25 Molecular, statistical, and kinetic theories in solid mechanics
74S10 Finite volume methods applied to problems in solid mechanics
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
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