Premium
A fully covariant four‐dimensional formulation in material space‐time
Author(s) -
Schnepp Johannes
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010155
Subject(s) - covariant transformation , tetrad , manifold (fluid mechanics) , lattice (music) , hyperelastic material , mathematics , space (punctuation) , mathematical analysis , classical mechanics , pure mathematics , physics , geometry , mathematical physics , computer science , finite element method , thermodynamics , mechanical engineering , acoustics , engineering , operating system
A fully covariant formulation for a hyperelastic solid as a four‐dimensional space‐time manifold is presented. It admits arbitrary coordinate transformations mixing space and time. The geometrical structure of the manifold is represented by a tetrad field. A variational formulation is given which uses the tetrad field as extra dependent variables. This formulation is able to describe a homogeneous stress state in a defect‐free crystal lattice. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom