Enhanced converse flexoelectricity in piezoelectric composites by coupling topology optimization with homogenization

Abstract

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Mathematical and computational modeling of flexoelectricity

“…This paper exemplifies how accurate computational methods can enable new material designs that exploit flexoelectricity in engineering applications, for instance to yield apparent piezoelectricity in metamaterials made of non-piezoelectric base materials 83 , given the inherent complexity of setups mobilizing field gradients. With this background, we expect that materials designs can be optimized geometrically and topo-logically 44,130,131 , and that ultimately the fundamental design principles of flexoelectric metamaterials can be distilled. There are some aspects that still hinder the quantitative evaluation of flexoelectricity.…”

“…Here, we focus on the formulation of flexoelectricity in centrosymmetric dielectrics for the sake of simplicity. More complete phenomenological formulations for flexoelectricity have also been proposed and studied in the literature 43,44 , which consider as well the linear couplings between strain and strain gradients, polarization and polarization gradients, and polarization gradients and strain gradients.…”

“…Nitsche [u, φ ] acting on the Dirichlet boundaries is introduced in the enthalpy functional in Eq. (44) or Eq. ( 60) to weakly enforce Dirichlet boundary conditions Eq.…”

The emancipation of flexoelectricity

“…Possible approaches of enhancing flexoelectric properties are discussed in polymers, 51,52,44,53 ceramics, [54][55][56][57] ferroelectrics, [58][59][60][61][62] and two-dimensional (2D) materials. 63,62 There is also an intriguing proposal regarding flexoelectricity in metals.…”