On the Passage from Atomistic Systems to Nonlinear Elasticity Theory
- We derive continuum limits of atomistic models in the realm of nonlinear elasticity theory rigorously as the interatomic distances tend to zero. In particular we obtain an integral functional acting on the deformation gradient in the continuum theory which depends on the underlying atomistic interaction potentials and the lattice geometry. The interaction potentials to which our theory applies are general finite range models which in particular can also account for multi-pole interactions and bond-angle dependent contributions. Furthermore, we discuss the applicability of the Cauchy-Born rule. Our class of limiting energy densities consists of general quasiconvex functions and the class of linearized limiting energies consistent with the Cauchy-Born rule consists of general quadratic forms not restricted by the Cauchy relations.
| Author: | Julian Braun, Bernd SchmidtGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-12756 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1672 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2012-03) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2012/03/06 |
| Tag: | Übergang von atomaren zu kontinuierlichen Systemen; Cauchy-Born Regel nonlinear elasticity theory; gamma-convergence; discrete-to-continuum limits; Cauchy-Born rule |
| GND-Keyword: | Gamma-Konvergenz; Nichtlineare Elastizitätstheorie; Variationsrechnung |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
