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Research Papers

Size-Dependent Flexoelectric Response of a Truncated Cone and the Consequent Ramifications for the Experimental Measurement of Flexoelectric Properties

[+] Author and Article Information
Qian Deng

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
Xi’an Jiaotong University,
Xi’an 710049, Shaanxi, China
e-mail: tonydqian@mail.xjtu.edu.cn

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 27, 2017; final manuscript received August 3, 2017; published online August 31, 2017. Assoc. Editor: M Taher A Saif.

J. Appl. Mech 84(10), 101007 (Aug 31, 2017) (8 pages) Paper No: JAM-17-1339; doi: 10.1115/1.4037552 History: Received June 27, 2017; Revised August 03, 2017

The flexoelectric effect is an electromechanical phenomenon that is universally present in all dielectrics and exhibits a strong size-dependency. Through a judicious exploitation of scale effects and symmetry, flexoelectricity has been used to design novel types of structures and materials including piezoelectric materials without using piezoelectric. Flexoelectricity links electric polarization with strain gradients and is rather difficult to estimate experimentally. One well-acknowledged approach is to fabricate truncated pyramids and/or cones and examine their electrical response. A theoretical model is then used to relate the measured experimental response to estimate the flexoelectric properties. In this work, we revisit the typical model that is used in the literature and solve the problem of a truncated cone under compression or tension. We obtained closed-form analytical solutions to this problem and examine the size and shape effects of flexoelectric response of the aforementioned structure. In particular, we emphasize the regime in which the existing models are likely to incur significant error.

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Figures

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Fig. 1

A truncated cone under compression

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Fig. 2

Change of deff as a function of the size h. The simplified model is for d(simp)eff.

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Fig. 3

Change of scaling rule with shape factor R=d1/d2

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Fig. 4

Shape effect for different sample sizes

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Fig. 5

Change of μ′ as a function of h for different shape factorR

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Fig. 6

Change of μ′ as a function of R for different h

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