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Applications of Higher-Order Continua to Size Effects in Bending: Theory and Recent Experimental Results

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Generalized Continua as Models for Classical and Advanced Materials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 42))

Abstract

In the context of static elasticity theory for isotropic materials under small deformations, different approaches of higher-order continuum mechanics are described. Considering generalized continua, the strain gradient-, micropolar- and surface elasticity theory are explained. Analytical solutions, such as the bending line, are derived for each extended theory, using the Euler–Bernoulli beam model. Atomic Force Microscopy investigations of the materials epoxy and the polymer SU-8, as well as flexural vibration analysis of aluminum foams were performed, to determine several additional material parameters. As a result, positive as well as negative size effects in dependency of the thickness and length are observed for micro-cantilevers.

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Notes

  1. 1.

    The displacement gradient is constant over the body.

  2. 2.

    www.nanonics.co.il, Jerusalem, Israel.

  3. 3.

    Physikalisch-Technische Bundesanstalt – Braunschweig, Germany.

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Acknowledgments

The present work is supported by (Deutsche Forschungsgemeinschaft) DFG under Grant MU 1752/33-1. The author like to thank the Fraunhofer Institute for Reliability and Microintegration Berlin for sample preparation and PTB-Braunschweig for AFM calibration.

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Authors and Affiliations

  1. Berlin University of Technology, Institute of Mechanics, Einsteinufer 5, 10587, Berlin, Germany

    Christian Liebold & Wolfgang H. Müller

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  1. Christian Liebold
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  2. Wolfgang H. Müller
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Correspondence to Christian Liebold .

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  1. Universität Magdeburg, Otto‐von‐Guericke, Magdeburg, Germany

    Holm Altenbach

  2. Mines ParisTech, Paris, France

    Samuel Forest

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Liebold, C., Müller, W.H. (2016). Applications of Higher-Order Continua to Size Effects in Bending: Theory and Recent Experimental Results. In: Altenbach, H., Forest, S. (eds) Generalized Continua as Models for Classical and Advanced Materials. Advanced Structured Materials, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-319-31721-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-31721-2_12

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