Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory. Rigorous Existence and Convergence Results for the Boundary Value Problems

Augsburger Schriften zur Mathematik, Physik und Informatik , Bd. 31

Julian Braun

ISBN 978-3-8325-4363-1
179 pages, year of publication: 2016
price: 36.00 €
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.

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Table of contents (PDF)


  • Partial Differential Equations
  • Atomistic Modeling
  • Discrete-to-Continuum Limits
  • Elastostatics and Elastodynamics
  • Cauchy-Born Rule


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