#### Description

A material is said to be flexoelectric when it polarizes in response to strain gradients. The phenomenon is well known in liquid crystals and biomembranes but has received less attention in hard materials such as ceramics. Here we derive the governing equations for a flexoelectric solid under small deformation. We assume a linear constitutive relation and use it to prove a reciprocal theorem for flexoelectric materials as well as to obtain a higher-order Navier equation in the isotropic case. The Navier equation is similar to that in Mindlin’s theory of strain-gradient elasticity. We also provide analytical solutions to several boundary value problems. We predict size-dependent electromechanical properties and flexoelectric modulation of material behavior. In the meantime, we also look at the interplay of flexo-electricity with defects such as dislocations and cracks in solids. Our results can be used to interpret experiments on flexoelectric materials which are becoming increasingly sophisticated due to the advent of nanoscale probes.

#### Recommended Citation

Mao, S.
(2014).
Insights into flexoelectricity from strain-gradient elasticity.
In A. Bajaj, P. Zavattieri, M. Koslowski, & T. Siegmund (Eds.).
*
Proceedings of the Society of Engineering Science 51st Annual Technical Meeting, October 1-3, 2014
*,
West Lafayette: Purdue University Libraries Scholarly Publishing Services, 2014.
https://docs.lib.purdue.edu/ses2014/mss/mmms/1

Insights into flexoelectricity from strain-gradient elasticity

A material is said to be flexoelectric when it polarizes in response to strain gradients. The phenomenon is well known in liquid crystals and biomembranes but has received less attention in hard materials such as ceramics. Here we derive the governing equations for a flexoelectric solid under small deformation. We assume a linear constitutive relation and use it to prove a reciprocal theorem for flexoelectric materials as well as to obtain a higher-order Navier equation in the isotropic case. The Navier equation is similar to that in Mindlin’s theory of strain-gradient elasticity. We also provide analytical solutions to several boundary value problems. We predict size-dependent electromechanical properties and flexoelectric modulation of material behavior. In the meantime, we also look at the interplay of flexo-electricity with defects such as dislocations and cracks in solids. Our results can be used to interpret experiments on flexoelectric materials which are becoming increasingly sophisticated due to the advent of nanoscale probes.