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Displaying similar documents to “Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics”

Atomistic to Continuum limits for computational materials science

Xavier Blanc, Claude Le Bris, Pierre-Louis Lions (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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The present article is an overview of some mathematical results, which provide elements of rigorous basis for some multiscale computations in materials science. The emphasis is laid upon atomistic to continuum limits for crystalline materials. Various mathematical approaches are addressed. The setting is stationary. The relation to existing techniques used in the engineering literature is investigated.

Abstract variational problems with volume constraints

Marc Oliver Rieger (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.