88th GAMM Annual Meeting

Flexoelectricity describes the linear coupling between the electric polarization and the mechanical strain gradient \nor that between the mechanical strain and the polarization gradient. [1] Unlike other electromechanical coupling \neffects such as piezoelectricity and electrostriction, which require the non-centrosymmetric of the structure, \nflexoelectric effect appears in materials of any symmetry. Due to the low value of flexoelectric coefficients, \nthe research on flexoelectricity in solids had long been overlooked, until a series of experimental observations \nabout large flexoelectric effect of ferroelectric materials were reported by Ma and Cross in last decades. [2] \nThe researchers are intrigued by these discoveries to study flexoelectricity and its applications, especially in \nnanoscale systems, which indicate bright prospect in utilizing flexoelectric effect of materials. \nIn this presentation, a continuum phase-field model of flexoelectricity is established in order to investigate \nthe influence of flexoelectricity on the polarization and mechanical properties of ferroelectric materials. To deal \nwith the high-order nature (strain gradient) originated from the flexoelectricity, a mixed finite element treatment \nis utilized. [3] For the ferroelectric properties, the polarization is regarded as the order parameter in phase field \nsimulation. The evolution of the polarization is governed by the time-dependent Ginzburg-Landau equation. \nBy 2-dimensional simulation, the comparison of the polarization between samples with and without flexoelectric \neffect is presented, which shows the importance of considering flexoelectric effect. The flexocoupling coefficients \nf11 and f44 shows different effect on domain configuration. Apart from that, the role of the boundary condition \nand the size effect are also studied. \nThe work of Shuai Wang is supported by the ’Excellence Initiative’ of the German Federal and State \nGovernments and the Graduate School of Computational Engineering at Technische Universität Darmstadt. \nREFERENCES \n[1] P. Zubko, G. Catalan and A.K. Tagantsev, “Flexoelectric effect in solids.” Annu. Rev. Mater. Sci., Vol. \n43, pp. 387-421, (2013). \n[2] W. Ma and L.E. Cross, “Flexoelectric polarization of barium strontium titanate in the paraelectric state.” \nAppl. Phys. Lett., Vol. 81, pp. 3440-3442, (2002). \n[3] E. Amanatidou and N. Aravas, “Mixed finite element formulations of strain-gradient elasticity problems.” \nComput. Methods Appl. Mech. Eng., 191(15), pp. 1723-1751, (2002).