On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models
type: Item
instance of: scholarly article
title: On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models
zbMATH Open document ID: 0819.73008
DOI: 10.1007/BF00043251
published in: Journal of Elasticity
publication date: 1994-08-10T00:00:00Z
review text: This paper is concerned with the one-dimensional nonlinear theory of elasticity. The authors present a consistent methodology for deriving higher order gradient continuum macroscopic models from the properties of discrete, periodic microstructure. Attention is focused on the model whose energy density involves only the second order gradient of the displacement. The accuracy of the continuum models is evaluated via examples where the boundary value problem of stretching a finite length bar is solved twice, once using the discrete model based on the exact model, and once using the corresponding continuum model based on the approximate one. The force-displacement diagrams and the equilibrium strain profiles for the localized solutions are compared. The stability of the solutions is also investigated.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74M25
zbMATH DE Number: 617002
zbMATH Keywords: periodic microstructure
zbMATH Keywords: energy density
zbMATH Keywords: boundary value problem
zbMATH Keywords: stretching
zbMATH Keywords: finite length bar
zbMATH Keywords: force-displacement diagrams
zbMATH Keywords: equilibrium strain profiles
zbMATH Keywords: localized solutions
author: Nicolas Triantafyllidis
author: Scott G. Bardenhagen
reviewed by: D. Ieşan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 617002