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

Numerical approach to a rate-independent model of decohesion in laminated composites

Zeman, Jan, Gruber, Pavel

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In this paper, we present a numerical approach to evolution of decohesion in laminated composites based on incremental variational problems. An energy-based framework is adopted, in which we characterize the system by the stored energy and dissipation functionals quantifying reversible and irreversible processes, respectively. The time-discrete evolution then follows from a solution of incremental minimization problems, which are converted to a fully discrete form by employing the conforming...

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.