Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Computational Mechanics of Generalized Continua

  • Stefan Kaessmair
  • Paul Steinmann
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_111-1

Synonyms

Definitions

Computational mechanics of generalized continua is a discipline concerned with computational methods for the solution of mechanical problems, extending/generalizing the classical Cauchy continuum as, for example, micromorphic or gradient continua. Its interdisciplinary character combines mechanics, mathematics, and computer sciences.

Overview

The classical Cauchy continuum modeling simple materials, cf. Noll (1958), is not capable of capturing material behavior that involves, e.g., size effects, localization phenomena, or the influence of the material’s substructure, i.e., the microstructure. This is not surprising; accounting only for the (dimensionless) first gradient of the deformation map, the classical continuum approach lacks an intrinsic length scale. Consequently, additional information is required to sufficiently characterize the response of non-simple materials.

Besides phenomenological approaches using internal...

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Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Chair of Applied MechanicsFriedrich–Alexander Universität Erlangen–NürnbergErlangenGermany

Section editors and affiliations

  • Samuel Forest
    • 1
  1. 1.Centre des Matériaux UMR 7633Mines ParisTech CNRSEvry CedexFrance