FLEXFRA: Modeling of Flexoelectricity (Strain and Polarization Gradients in Piezo- and Ferroelectric Materials), with Emphasis on Fracture

• Applicant: Dr. Sergey Kozinov, Ph.D.
• Subject Area: Mechanics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 451375510

The aim of the project is fundamental theoretical and numerical research on the intensively developing discipline of flexoelectric material behavior (higher-order electromechanical coupling) with particular emphasis on fracture behavior. Flexoelectricity induces polarization due to strain gradients in the material and reversely strain response to polarization gradient. This nonuniform strain/polarization breaks centrosymmetry, meaning that unlike in piezoelectricity, flexoelectric effects can occur in structures with arbitrary crystal symmetry. Thus, flexoelectricity can be a substitute for piezoelectricity at the micro- and nanoscales in dielectric materials. This is essential in nano- and microelectronic devices considering that the strain gradient becomes very large at the nanoscale, since it is inversely proportional to the length scale of the structure. Strong gradients of electromechanical fields occur inevitably near sharp edges, electrodes and crack-like defects, which requires special fracture mechanical analyses and assessment. Additional challenges appear in the case of piezoelectric materials, where an auxiliary flexoelectric contribution to electromechanical coupling is difficult to measure separately. Moreover, the domain reorientation in ferroelectrics occurs in regions with high electromechanical field concentrations where the flexoelectric effect may influence the switching processes. Considering all currently open scientific questions and debatable issues, a consistent approach is proposed pursuing a systematic derivation of analytical solutions and numerical techniques, which allows for the separation of each effect with subsequent induction of their interaction: 1) analytical derivations for the near crack tip fields, including anisotropy and piezoelectric coupling, 2) phase-field modeling of ferroelectric material behavior, including polarization and strain gradients, with application to fracture problems, and 3) mixed finite-element formulations for the strain gradient elasticity extended towards the piezo- and ferroelectric (micromechanical switching model) contributions. From the obtained research results, better knowledge of these coupled electromechanical effects in smart materials is expected, which is important for applications in nano- and micro-devices for sensors, actuators, digital storage, energy transducers, and flexible electronics. This applies as well to their functional design as to issues of their reliability and lifetime.

• DFG Programme: Research Grants