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Research Papers

A Theory of Flexoelectric Membranes and Effective Properties of Heterogeneous Membranes

[+] Author and Article Information
P. Mohammadi

Department of Mechanical Engineering,
University of Houston,
Houston, TX 77204

L. P. Liu

Department of Mathematics,
Department of Mechanical
Aerospace Engineering,
Rutgers University,
Newark, NJ 08854

P. Sharma

Department of Mechanical Engineering,
Department of Physics,
University of Houston,
Houston, TX 77204
e-mail: psharma@uh.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 5, 2013; final manuscript received February 14, 2013; published online August 22, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(1), 011007 (Aug 22, 2013) (11 pages) Paper No: JAM-13-1008; doi: 10.1115/1.4023978 History: Received January 05, 2013; Revised February 14, 2013

Recent developments in flexoelectricity, especially in nanostructures, have lead to several interesting notions such as piezoelectric materials without using piezoelectric materials and enhanced energy harvesting at the nanoscale, among others. In the biological context also, membrane flexoelectricity has been hypothesized to play an important role, e.g., biological mechanotransduction and hearing mechanisms, among others. In this paper, we consider a heterogeneous flexoelectric membrane and derive the homogenized or renormalized flexoelectric, dielectric, and elastic response, therefore, relating the corresponding effective electromechanical properties to its microstructural details. Our work allows design of a microstructure to tailor flexoelectric response, and an illustrative example is given for biological membranes.

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Topics: Membranes
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References

Figures

Grahic Jump Location
Fig. 1

Mechanism of flexoelectricity in 2D crystalline membranes such as graphene (adapted from Dumitrica et al. [31])

Grahic Jump Location
Fig. 2

A representative volume element of two-phase heterogeneous membrane: (a) a simple laminate; (b) inclusions embedded in a continuous matrix

Grahic Jump Location
Fig. 3

Effective flexoelectric of protein inclusions in lipid bilayer: (a) the effective constant γe = fe/ae as a function of aspect ratio of protein ellipsoid. The volume fraction of protein is assumed to be 0.1, and (b) the effective constant γe = fe/ae as a function of volume fraction of inclusion. The solid curve is predicted by Eq. (4.38); the dashed curve is calculated by Eq. (5.2) assuming ax/ay = 1.

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