A. Abdollahi, P. Christian, M. D. Daniel, M. Arroyo, and A. I. Irene, Computational evaluation of the flexoelectric effect in dielectric solids, Journal of Applied Physics, vol.116, issue.9, p.93502, 2014.
DOI : 10.1063/1.4893974

J. Aboudi, Micro-electromechanics of soft dielectric matrix composites, International Journal of Solids and Structures, vol.64, issue.65, pp.64-6530, 2015.
DOI : 10.1016/j.ijsolstr.2015.03.011

R. Ahluwalia, A. K. Tagantsev, P. Yudin, N. Setter, N. Ng et al., Influence of flexoelectric coupling on domain patterns in ferroelectrics, Physical Review B, vol.89, issue.17, p.174105, 2014.
DOI : 10.1103/PhysRevB.89.174105

E. Amanatidou and N. Aravas, Mixed finite element formulations of strain-gradient elasticity problems, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.15-16, pp.1723-1751, 2002.
DOI : 10.1016/S0045-7825(01)00353-X

J. Y. Fu, W. Zhu, N. Li, and L. E. Cross, Experimental studies of the converse flexoelectric effect induced by inhomogeneous electric field in a barium strontium titanate composition, Journal of Applied Physics, vol.100, issue.2, p.24112, 2006.
DOI : 10.1063/1.2219990

F. Carpi, S. Bauer, and D. Rossi, Stretching Dielectric Elastomer Performance, Science, vol.330, issue.6012, pp.1759-1761, 2010.
DOI : 10.1126/science.1194773

Y. Chen, M. Pani, F. Taddei, and C. Mazzà, Large-Scale Finite Element Analysis of Human Cancellous Bone Tissue Micro Computer Tomography Data: A Convergence Study, Journal of Biomechanical Engineering, vol.136, issue.10, p.136101013, 2014.
DOI : 10.1115/1.4028106

B. Chu and D. R. Salem, Flexoelectricity in several thermoplastic and thermosetting polymers, Applied Physics Letters, vol.101, issue.10, p.103905, 2012.
DOI : 10.1063/1.4750064

L. E. Cross, Flexoelectric effects: Charge separation in insulating solids subjected to elastic strain gradients, Journal of Materials Science, vol.60, issue.8, pp.53-63, 2006.
DOI : 10.1007/s10853-005-5916-6

Q. D. Deng, L. P. Liu, and P. Sharma, Flexoelectricity in soft materials and biological membranes, Journal of the Mechanics and Physics of Solids, vol.62, pp.209-227, 2014.
DOI : 10.1016/j.jmps.2013.09.021

V. Dominguez and F. J. Saya, A simple Matlab implementation of the Argyris element, ACM T. Math. Software, vol.35, issue.2, p.16, 2008.

A. Dorfmann and R. W. Ogden, Nonlinear electroelasticity, Acta Mechanica, vol.174, issue.3-4, pp.167-183, 2005.
DOI : 10.1007/s00707-004-0202-2

G. Gallone, F. Galantini, and F. Carpi, Perspectives for new dielectric elastomers with improved electromechanical actuation performance: composites versus blends, Polymer International, vol.96, issue.3, pp.400-406, 2010.
DOI : 10.1002/pi.2765

S. Y. Hu and L. Q. Chen, A phase-field model for evolving microstructures with strong elastic inhomogeneity, Acta Materialia, vol.49, issue.11, p.1879, 2001.
DOI : 10.1016/S1359-6454(01)00118-5

J. Huang, T. Lu, J. Zhu, D. R. Clarke, and Z. Suo, Large, uni-directional actuation in dielectric elastomers achieved by fiber stiffening, Applied Physics Letters, vol.100, issue.21, p.211901, 2012.
DOI : 10.1063/1.4720181

T. A. Gisby, I. A. Anderson, B. M. O-'brien, T. G. Mckay, and E. P. Calius, Multifunctional dielectric elastomer artificial muscles for soft and smart machines, J. Appl. Phys, vol.112, p.41101, 2012.

Y. Bazilevs, J. Cotterel, and T. J. Hughes, Isogeometric analysis: Toward integration of CAD and FEA, 2009.

J. P. Jaric, D. Kuzmanovic, and Z. Golubovic, On tensors of elasticity, Theoretical and Applied Mechanics, vol.35, issue.1-3, pp.119-136, 2008.
DOI : 10.2298/TAM0803119J

S. M. Kogan, Piezoelectric effect during inhomogeneous deformation and acoustic scattering of carriers in crystals, Sov. Phys. Solid Stat, vol.5, issue.10, 1964.

S. Krichen and P. Sharma, Flexoelectricity: A Perspective on an Unusual Electromechanical Coupling, Journal of Applied Mechanics, vol.83, issue.3, pp.30801-30802, 2016.
DOI : 10.1115/1.4032378

W. Li and C. M. Landis, Deformation and instabilities in dielectric elastomer composites, Smart Materials and Structures, vol.21, issue.9, p.94006, 2012.
DOI : 10.1088/0964-1726/21/9/094006

L. P. Liu, An energy formulation of continuum magneto-electro-elasticity with applications, Journal of the Mechanics and Physics of Solids, vol.63, pp.451-480, 2014.
DOI : 10.1016/j.jmps.2013.08.001

O. Lopez-pamies, Elastic dielectric composites: Theory and application to particle-filled ideal dielectrics, Journal of the Mechanics and Physics of Solids, vol.64, pp.61-82, 2014.
DOI : 10.1016/j.jmps.2013.10.016

W. Ma and L. E. Cross, Flexoelectric polarization of barium strontium titanate in the paraelectric state, Applied Physics Letters, vol.81, issue.18, pp.3440-3442, 2002.
DOI : 10.1063/1.1518559

W. Ma and L. E. Cross, Strain-gradient-induced electric polarization in lead zirconate titanate ceramics, Applied Physics Letters, vol.82, issue.19, pp.3923-3925, 2003.
DOI : 10.1063/1.1570517

T. G. Mckay, B. M. O-'brien, E. P. Calius, and I. A. Anderson, Soft generators using dielectric elastomers, Applied Physics Letters, vol.98, issue.14, p.142903, 2011.
DOI : 10.1063/1.3572338

R. M. Mcmeeking and C. M. Landis, Electrostatic Forces and Stored Energy for Deformable Dielectric Materials, Journal of Applied Mechanics, vol.72, issue.4, pp.581-590, 2005.
DOI : 10.1115/1.1940661

H. S. Park, Z. Suo, J. Zhuo, and P. A. Klein, A dynamic finite element method for inhomogeneous deformation and electromechanical instability of dielectric elastomer transducers, International Journal of Solids and Structures, vol.49, issue.15-16, pp.2187-2194, 2012.
DOI : 10.1016/j.ijsolstr.2012.04.031

H. S. Park and T. D. Nguyen, Viscoelastic effects on electromechanical instabilities in dielectric elastomers, Soft Matter, vol.141, issue.4, pp.1031-1042, 2013.
DOI : 10.1039/C2SM27375F

R. Pelrine, R. Kornbluh, Q. B. Pei, and J. Joseph, High-Speed Electrically Actuated Elastomers with Strain Greater Than 100%, Science, vol.287, issue.5454, pp.836-839, 2000.
DOI : 10.1126/science.287.5454.836

A. W. Richards and G. M. , Constitutive Modeling of Electrostrictive Polymers Using a Hyperelasticity-Based Approach, Journal of Applied Mechanics, vol.77, issue.1, p.14502, 2010.
DOI : 10.1115/1.3173766

N. D. Sharma, R. Maraganti, and P. Sharma, On the possibility of piezoelectric nanocomposites without using piezoelectric materials, Journal of the Mechanics and Physics of Solids, vol.55, issue.11, pp.2328-2350, 2007.
DOI : 10.1016/j.jmps.2007.03.016

J. Y. Shu, W. E. King, and N. A. Fleck, Finite elements for materials with strain gradient effects, International Journal for Numerical Methods in Engineering, vol.9, issue.3, pp.373-391, 1999.
DOI : 10.1002/(SICI)1097-0207(19990130)44:3<373::AID-NME508>3.0.CO;2-7

Z. Suo, X. Zhao, and W. H. Greene, A nonlinear field theory of deformable dielectrics, Journal of the Mechanics and Physics of Solids, vol.56, issue.2, pp.467-486, 2008.
DOI : 10.1016/j.jmps.2007.05.021

K. Y. Volokh, On Electromechanical Coupling in Elastomers, Journal of Applied Mechanics, vol.79, issue.4, p.44507, 2012.
DOI : 10.1115/1.4006057

Q. W. Wang, Z. G. Suo, and X. H. Zhao, Bursting drops in solid dielectrics caused by high voltages, Nature Communications, vol.107, p.1157, 2012.
DOI : 10.1038/ncomms2178

Y. U. Wang, Y. M. Jin, and A. G. Khachaturyan, Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid, Journal of Applied Physics, vol.92, issue.3, p.1351, 2002.
DOI : 10.1063/1.1492859

L. Yang and K. Dayal, A completely iterative method for the infinite domain electrostatic problem with nonlinear dielectric media, Journal of Computational Physics, vol.230, issue.21, pp.7821-7829, 2011.
DOI : 10.1016/j.jcp.2011.07.001

P. V. Yudin and A. K. Tagantsev, Fundamentals of flexoelectricity in solids, Nanotechnology, vol.24, issue.43, p.432001, 2013.
DOI : 10.1088/0957-4484/24/43/432001

X. Zhao, W. Hong, and Z. Suo, Electromechanical hysteresis and coexistent states in dielectric elastomers, Physical Review B, vol.76, issue.13, p.134113, 2007.
DOI : 10.1103/PhysRevB.76.134113

X. Zhao and Z. Suo, Electrostriction in elastic dielectrics undergoing large deformation, Journal of Applied Physics, vol.104, issue.12, p.123530, 2008.
DOI : 10.1063/1.3031483

X. Zhao and Z. Suo, Theory of Dielectric Elastomers Capable of Giant Deformation of Actuation, Physical Review Letters, vol.104, issue.17, p.178302, 2010.
DOI : 10.1103/PhysRevLett.104.178302

G. P. Zubko, A. R. Catalan, P. Buckley, L. Welche, and J. F. Scott, Straingradient induced polarization in SrTiO3 single crystals, Phys. Rev. Lett, issue.16, p.99167601, 2007.