JournalsifbVol. 11, No. 3pp. 421–446

Continuum limits of atomistic energies allowing smooth and sharp interfaces in 1D elasticity

  • Carlos Mora-Corral

    Bizkaia Technology Park, Derio (Vizcaya), Spain
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Abstract

We present two atomistic models for the energy of a one-dimensional elastic crystal. We assume that the macroscopic displacement equals the microscopic one. The energy of the first model is given by a two-body interaction potential, and we assume that the atoms follow a continuous and piecewise smooth macroscopic (continuum) deformation. We calculate the first terms of the Taylor expansion (with respect to the parameter representing the interatomic distance) of the atomistic energy, and deduce that the coefficients of that Taylor expansion represent, respectively, an elastic energy, a sharp-interface energy, and a smooth-interface energy. The second atomistic model is a variant of the first one, and its Taylor expansion predicts, in addition, a new term that accounts for the repulsion force between two sharp interfaces.

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Carlos Mora-Corral, Continuum limits of atomistic energies allowing smooth and sharp interfaces in 1D elasticity. Interfaces Free Bound. 11 (2009), no. 3, pp. 421–446

DOI 10.4171/IFB/217