- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2009
3
Continuum limits of atomistic energies allowing smooth and sharp interfaces in 1D elasticity
Carlos
Mora-Corral
Bizkaia Technology Park, DERIO (VIZCAYA), SPAIN
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.
Partial differential equations
Mechanics of particles and systems
Statistical mechanics, structure of matter
General
421
446
10.4171/IFB/217
http://www.ems-ph.org/doi/10.4171/IFB/217