A model for elastic flexoelectric materials including strain gradient effects. (February 2016)

• Record Type: Journal Article
• Authors: Enakoutsa, Koffi; Corte, Alessandro Della; Giorgio, Ivan
• Other Names: Eremeyev Victor A guest-editor.; Porubov Alexey V guest-editor.; Placidi Luca guest-editor.
• Is Part Of: Mathematics and mechanics of solids. Volume 21:Number 2(2016:Mar.)
• Page Start: 242
• Page End: 254
• Publication Date: 2016-02
• Subjects: Flexoelectric materials -- second gradient theory -- constitutive equations -- electro-mechanical coupling; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286515588638
• Languages: English
• ISSNs: 1081-2865

Abstract

A constitutive model for elastic flexoelectric materials under small deformation based on second gradient continuum theory is developed, using a Toupin-like variational formulation to simultaneously obtain constitutive relations, balance equations and boundary conditions. The model includes three different electromechanical "stresses": a higher-order stress, an extended local electric force and a generalized Cauchy stress tensor. The constitutive equations of the model are obtained by postulating an internal energy density function which depends on both the strain and its gradient as well as the polarization. Finally, as an application of the model, we derive the explicit analytical expressions of the polarization and displacement vector fields for the problem of the polarization induced over a thin spherical shell subjected to hydrostatic loading conditions.