David Codony defended his PhD thesis Mathematical and computational modeling of flexoelectricity at mesoscopic and atomistic scales (pdf) on March 1st 2021, supervised by Professor Irene Arias in the Mechanics of Electroactive Materials research group in LaCàN, within the UPC doctoral program in Applied Mathematics. During his doctoral training he also joined the MP&M group in Georgia Tech (Atlanta, GA, USA) led by Professor Phanish Suryanarayana as a visiting scholar for 5 months. He is currently a Severo Ochoa postdoctoral trainee in the group of Mechanics of Electroactive Materials at CIMNE, and part-time associate professor at UPC.
Thesis summary
Flexoelectricity is the twoway coupling between polarization and strain gradients. Conversely, it couples also polarization gradients and strain. It has emerged as an alternative to piezoelectricity at small scales. Piezoelectricity, the linear coupling between polarization and strain, is limited by symmetry and thus sustained only by materials with a non-centrosymmetric atomic or molecular structure. This introduces limiting trade-offs regarding performance, toughness, toxicity or operating temperature. For instance, current electromechanical transduction technologies in sensors, actuators and energy harvesters widely across industries rely strongly on piezoelectric ceramics such as PZT, with high contents of toxic lead. Being a universal property of all dielectrics, flexoelectricity broadens the class of materials for
electromechanical transduction at small scales, where gradients are sufficiently large. Hence, it has the potential to become a key mechanism for cleaner and safer energy devices [1].
Harnessing flexoelectricity as a functional property requires complex gradient-generating geometries with sub/micron features, calling for advanced modeling and computational tools which were not available just a few years back. In this PhD thesis, we develop an advanced computational infrastructure to quantify flexoelectricity in solids, focusing on continuum models but also exploring multiscale aspects.
On the one hand, we develop a mathematical and computational model for flexoelectricity at the continuum level. Mathematically, flexoelectricity is modeled as a coupled system of fourth-order PDEs. The high-order nature of the problem in combination with designs spaces necessarily involving complex geometries, calls for advanced computational techniques beyond standard finite element methods. This novel computational infrastructure is able to predict the performance of engineered devices for electromechanical transduction at sub-micron scales, where flexoelectricity is always present, without any particular restriction in geometry, material choice, boundary conditions or nonlinearity [2-4]. It is used to explore different means to harness flexoelectricity towards the development of breakthrough applications in nanotechnology [5]. Of particular interest is the design of flexoelectricity-based metamaterials producing a significant piezoelectric-like response from non-piezoelectric base-materials [6]. These metamaterials open up the way for light-weight chemically and mechanically biocompatible electromechanical devices.
On the other hand, we also explore flexoelectricity from first principles and establish the connection between the continuum and the atomistic description. We propose a novel methodology to quantify the flexoelectric properties of dielectric materials [7] by connecting the proper interpretation of ab-initio atomistic simulations with the proposed models at a coarser, continuum scales. The developed approach sheds light on a controversial topic within the density functional theory community, where large disagreements among different theoretical derivations are typically found. The ab-initio computations serve not only to extract material parameters for the continuum models [8], but also to validate their inherent assumptions regarding the relevant physics at the nanoscale.
References
[1] European Patent application «LATTICE STRUCTURE WITH PIEZOELECTRIC BEHAVIOR, A FORCE OR MOVEMENT SENSOR AND AN ACTUATOR CONTAINING SAID LATTICE STRUCTURE», 20382094.9 (EP3866214).
[2] D. Codony, O. Marco, S. Fernández-Méndez, and I. Arias. An Immersed Boundary Hierarchical B-spline method for flexoelectricity. Comput. Meth. Appl. Mech. Eng. 354, 750 (2019).
[3] J. Barceló-Mercader, D. Codony, S. Fernández-Méndez, and I. Arias, Weak enforcement of interface continuity and generalized periodicity in high-order electromechanical problems, Int J Numer Methods Eng 1-23 (2021).
[4] D. Codony, A. Mocci, J. Barceló-Mercader, I. Arias. Mathematical and computational modeling of flexoelectricity, J. Appl Phys, 130:000000 (2021).
[5] D. Codony, P. Gupta, O. Marco, and I. Arias. Modeling flexoelectricity in soft dielectrics at finite deformation. J. Mech. Phys. Solids 146, 104182 (2020).
[6] A. Mocci, J. Barceló-Mercader, D. Codony, and I. Arias. Geometrically polarized architected dielectrics with apparent piezoelectricity. J. Mech. Phys. Solids 157, 104643 (2021).
[7] D. Codony, I. Arias, and P. Suryanarayana. Transversal flexoelectric coeffcient for nanostructures at finite deformations from first principles. Phys. Rev. Materials 5, L030801 (2021).
[8] S. Kumar, D. Codony, I. Arias, and P. Suryanarayana. Transversal flexoelectric coeffcients for fifty select atomic monolayers from first principles. Nanoscale 13, 1600-1607, 2020.