Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory

Rigorous Existence and Convergence Results for the Boundary Value Problems

By (author) Julian Braun

Book cover: Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory

Extent: 179 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Series: Augsburger Schriften zur Mathematik, Physik und Informatik

Series volume number: 31

Language: English

Paperback (Published)

(November 2016)

ISBN: 9783832543631

5.71 x 8.27 inches

Price: $54.00

In stock

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Synopsis
Contributing Authors

The nonlinear elastic behavior of solid materials is often described in the context of continuum mechanics. Alternatively, one can try to determine the behavior of every single atom in the material. Classically, the connection between these two types of models is made with the Cauchy-Born rule. The aim of this book is to provide good criteria for the Cauchy-Born rule to be true and to make the connection between continuum and atomistic models precise. In particular, this includes rigorous proofs for the existence of solutions to the atomistic boundary value problem and their convergence to the corresponding continuum solutions in the limit of small interatomic distances.

By (author) Julian Braun

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