Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory

Download or read book Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory written by Julian Braun and published by Logos Verlag Berlin GmbH. This book was released on 2016-11-15 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.