Qualitative properties of a continuum theory for thin films
Bernd Schmidt (2008)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “Atomistic to Continuum limits for computational materials science ”
Qualitative properties of a continuum theory for thin films
Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics
Xavier Blanc, Claude Le Bris, Frédéric Legoll (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have recently been proposed. They aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical ground for such a coupling in a one-dimensional setting. We briefly study the general case of a convex energy, and next concentrate on a specific example of a nonconvex energy, the Lennard-Jones...
Non-local continuum thermodynamic extensions of crystal plasticity to include the effects of geometrically-necessary dislocations on the material behaviour.
Svendsen, B. (2000)
Rendiconti del Seminario Matematico
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Multiscale Materials Modelling: Case Studies at the Atomistic and Electronic Structure Levels
Emilio Silva, Clemens Först, Ju Li, Xi Lin, Ting Zhu, Sidney Yip (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
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Although the intellectual merits of computational modelling across various length and time scales are generally well accepted, good illustrative examples are often lacking. One way to begin appreciating the benefits of the multiscale approach is to first gain experience in probing complex physical phenomena at one scale at a time. Here we discuss materials modelling at two characteristic scales separately, the atomistic level where interactions are specified through classical potentials...