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2015 | OriginalPaper | Chapter

9. Are Microcontinuum Field Theories of Elasticity Amenable to Experiments? A Review of Some Recent Results

Authors : Christian Liebold, Wolfgang H. Müller

Published in: Differential Geometry and Continuum Mechanics

Publisher: Springer International Publishing

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Abstract

It is well known that the material behavior at the micro- and even more at the nano-scale is size dependent, which is, for example, reflected in a stiffer elastic response. Thus modeling of micro- and nanoelectromechanical systems should be ready to incorporate size dependency as well. However, the classical Boltzmann continuum fails to reproduce the size effect. In this work special attention is paid to higher gradient theories such as the strain gradient theory (of Mindlin’s form-II), the modified strain gradient theory and the couple stress theory for linear elasticity. In particular, the latter will also be investigated in terms of finite elements. A confrontation to the Cosserat- or micropolar theory, the non-local continuum, the fractional calculus and the surface elasticity is carried out.

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previous chapter Non-metricity and the Nonlinear Mechanics of Distributed Point Defects

next chapter On the Variational Limits of Lattice Energies on Prestrained Elastic Bodies

Physical linearity denotes a linear dependency of the stress measures on the strain measures.

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Title: Are Microcontinuum Field Theories of Elasticity Amenable to Experiments? A Review of Some Recent Results
Authors: Christian Liebold
Wolfgang H. Müller
Publisher: Springer International Publishing
Book: Differential Geometry and Continuum Mechanics
Print ISBN: 978-3-319-18572-9

Electronic ISBN: 978-3-319-18573-6

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-319-18573-6_9

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