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2016 | OriginalPaper | Chapter

2. Continuum Mechanics in One Dimension

Authors : Konstantin Naumenko, Holm Altenbach

Published in: Modeling High Temperature Materials Behavior for Structural Analysis

Publisher: Springer International Publishing

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Abstract

This chapter gives a short introduction to the continuum mechanics applied to the uni-axial stress state.

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previous chapter Introduction
next chapter Elementary Uni-axial Constitutive Models
Footnotes
1
The deformation gradient is usually not introduced within the one-dimensional theory of rods. Here we introduce this and other quantities to explain basic ideas of continuum mechanics.
 
2
Body forces like the force of gravity are not included here for the sake of brevity.
 
3
Here and in the following derivations we assume that N and other field variables are smooth functions. In the case of finite jumps one should apply Eq. (2.1.14) and introduce the jump conditions.
 
Literature
Altenbach H, Naumenko K, Zhilin PA (2005) A direct approach to the formulation of constitutive equations for rods and shells. In: Pietraszkiewicz W, Szymczak C (eds) Shell Structures: Theory and Applications, Taylor & Francis, Leiden, pp 87–90
Altenbach H, Bîrsan M, Eremeyev VA (2013) Cosserat-type rods. In: Eremeyev VA, Altenbach H (eds) Generalized Continua from the Theory to Engineering Applications, Springer, pp 179–248
Ericksen J (1998) Introduction to the Thermodynamics of Solids, Applied Mathematical Sciences, vol 131. Springer
Green AE, Naghdi PM, Wenner ML (1974a) On the theory of rods. I. Derivations from the three-dimensional equations. Proc R Soc Lond A Math Phys Sci 337(1611):451–483
Green AE, Naghdi PM, Wenner ML (1974b) On the theory of rods. II. Developments by direct approach. Proc R Soc Lond A Math Phys Sci 337(1611):485–507
Müller I (2007) A history of thermodynamics: the doctrine of energy and entropy. Springer
Zhilin PA (2006) Nonlinear theory of thin rods. In: Indeitsev D, Ivanova E, Krivtsov A (eds) Advanced Problems in Mechanics, vol 2. Nestor, St Petersburg, pp 227–249
Metadata
Title
Continuum Mechanics in One Dimension
Authors
Konstantin Naumenko
Holm Altenbach
Copyright Year
2016
Book
Modeling High Temperature Materials Behavior for Structural Analysis

Print ISBN: 978-3-319-31627-7

Electronic ISBN: 978-3-319-31629-1

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-31629-1_2

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