The finite element method (FEM) is developed to analyse 2-D crack problems in piezoelectric solids that exhibit the size-effect. This phenomenon, which typically occurs in micro/nano electronic structures, is described by the strain- and electric field-gradients in the constitutive equations. The variational principle with the appropriate boundary conditions is employed to derive the governing equations, from which the FEM formulation with C1-continuous elements is developed and implemented. An example is presented to demonstrate the effects of the strain- and electric intensity-gradients on the electro-mechanical behavior of the cracked solid.

2D crack problems, Converse flexoelectricity, Direct, Electric intensity vector gradient, Strain
Key Engineering Materials
Department of Mechanical and Aerospace Engineering

Sladek, J. (Jan), Sladek, V. (Vladimir), Wünsche, M. (Michael), & Tan, C. (2018). Flexoelectric effect for cracks in piezoelectric solids. In Key Engineering Materials. doi:10.4028/