Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: A Theory of Flexoelectric Membranes and Effective Properties of Heterogeneous Membranes J. Appl. Mech. 2013;81(1):011007-011007-11. doi:10.1115/1.4023978 Figure Legend: Mechanism of flexoelectricity in 2D crystalline membranes such as graphene (adapted from Dumitrica et al. [31])

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: A Theory of Flexoelectric Membranes and Effective Properties of Heterogeneous Membranes J. Appl. Mech. 2013;81(1):011007-011007-11. doi:10.1115/1.4023978 Figure Legend: A representative volume element of two-phase heterogeneous membrane: (a) a simple laminate; (b) inclusions embedded in a continuous matrix

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: A Theory of Flexoelectric Membranes and Effective Properties of Heterogeneous Membranes J. Appl. Mech. 2013;81(1):011007-011007-11. doi:10.1115/1.4023978 Figure Legend: 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.