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From molecular models to continuum mechanics. (English) Zbl 1028.74005
Summary: We present here a limiting process allowing us to write some continuum mechanics models as a natural asymptotic of molecular models. The approach is based on the hypothesis that the macroscopic displacement is equal to the microscopic one. We carry out the corresponding calculations in the case of two-body energies, including higher-order terms, and also in the case of Thomas-Fermi type models.

MSC:
74A25 Molecular, statistical, and kinetic theories in solid mechanics
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
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