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Technical Brief

Multiple Neutral Axes in Bending of a Multiple-Layer Beam With Extremely Different Elastic Properties

[+] Author and Article Information
Yan Shi

State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics & Astronautics,
Nanjing 210016, China
Department of Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60208
Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
Center for Engineering and Health,
Northwestern University,
Evanston, IL 60208
Skin Disease Research Center,
Northwestern University,
Evanston, IL 60208

John A. Rogers

Department of Materials Science and Engineering,
Frederick Seitz Materials Research Laboratory,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

Cunfa Gao

State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics & Astronautics,
Nanjing 210016, China

Yonggang Huang

Department of Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60208
Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
Center for Engineering and Health,
Northwestern University,
Evanston, IL 60208
Skin Disease Research Center,
Northwestern University,
Evanston, IL 60208
e-mail: y-huang@northwestern.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 4, 2014; final manuscript received August 25, 2014; accepted manuscript posted September 2, 2014; published online September 17, 2014. Assoc. Editor: Arun Shukla.

J. Appl. Mech 81(11), 114501 (Sep 17, 2014) (3 pages) Paper No: JAM-14-1293; doi: 10.1115/1.4028465 History: Received July 04, 2014; Accepted August 25, 2014; Revised August 25, 2014

The multi-layer beam consisted of materials with extremely different elastic properties, such as silicon and Polydimethylsiloxane (PDMS), has many important applications. The Kirchhoff assumption that the straight lines normal to the midsurface remain normal after deformation does not hold any more. The energy method is used to establish a simple analytic model for multi-layered structures with extremely different elastic properties. The analytic model is validated by finite element analysis.

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References

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Figures

Grahic Jump Location
Fig. 1

Schematic illustration of a multilayer beam composited of materials with extremely different elastic properties

Grahic Jump Location
Fig. 2

Comparison of the strain distribution from FEA [10] and present theory

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