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Second‐neighbor interactions in classical field theories: invariance of the relative power and covariance
Author(s) -
Mariano Paolo Maria
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4057
Subject(s) - mathematics , covariance , axiom , isomorphism (crystallography) , scale invariance , dissipation , field (mathematics) , manifold (fluid mechanics) , statistical physics , theoretical physics , pure mathematics , geometry , physics , quantum mechanics , statistics , mechanical engineering , chemistry , crystal structure , engineering , crystallography
We propose a model‐building framework unifying those continuum models of condensed matter accounting for second‐neighbor interactions. A notion of material isomorphism justifies restrictions that we impose to changes in observers on the material manifold. In the presence of dissipation due to evolution of inhomogeneities, we extend the notion of relative power including hyperstresses and derive pertinent balance equations by exploiting an invariance axiom. The scheme presented here permits an extension of the multi‐field model‐building framework for complex materials to account at a gross scale for second‐neighbor microstructural interactions. Copyright © 2016 John Wiley & Sons, Ltd.