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Higher‐Order Terms in the Homogenized Stress‐Strain Relation of Periodic Elastic Media
Author(s) -
Gambin B.,
Kröner E.
Publication year - 1989
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221510211
Subject(s) - relation (database) , displacement (psychology) , displacement field , stress–strain curve , mathematical analysis , order (exchange) , stress (linguistics) , mathematics , field (mathematics) , strain (injury) , classical mechanics , stress field , physics , pure mathematics , finite element method , computer science , thermodynamics , medicine , psychology , linguistics , philosophy , deflection (physics) , finance , database , economics , psychotherapist
Applying the method of two‐scale asymptotic expansions to the displacement field in periodic elastic structures the completed macroscopic stress‐strain relation of such media is derived. This relation contains beside the usually considered local part also weakly nonlocal contributions in the form of strain gradients up to infinite order. Formulae for the determination of the pertaining homogenized material tensors are derived.