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Research Publications

22

Unified open-boundary electrostatics in real-space density functional theory

ArXiv Preprints

Kumar R., Codony D., Suryanarayana P., Sharma A. (2026)

We present an electrostatic formulation in real-space density functional theory that provides a systematic and unified treatment of the open-boundary electrostatics of isolated and partially periodic systems, including in the presence of an applied uniform electric field along the open (finite) directions. ...

21

High-order flexoelectric beams and bars with transversal strain and axial voltage

(Accepted for publication) European Journal of Mechanics - A/Solids

Greco F., Codony D., Mohammadi H., Arias I. (2026)

Flexoelectric beams become electromechanically active at small scales, but most one-dimensional models neglect through-thickness electric and strain boundary layers, transverse deformation, and the longitudinal electric field. We develop a high-order analytical framework for flexoelectric Euler–Bernoulli beams and bars that retains these ingredients, ...

20

Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations

European Journal of Mechanics - A/Solids

Sky A., Codony D., Rudykh S., Zilian A., Bordas S. P. A., Neff P. (2026)

We propose geometrically nonlinear (finite) continuum models of flexomagnetism based on the Cosserat micropolar and its descendent couple-stress theory. These models introduce the magneto-mechanical interaction by coupling the micro-dislocation tensor of the micropolar model with the magnetisation vector ...

19

From bulk to surface: The emergence of surface effects in nanoscale dielectrics

IMTech Newsletter 2025

Codony D. (2026)

Our recent work has shifted the focus from the bulk of the material to its surfaces. We have noticed that in purely flexoelectric samples, the simple presence of a free surface breaks the material’s symmetry, causing boundary layers to naturally emerge in the strain and electric field profiles, even if bulk effects only ...

18

Continuum and computational modeling of surface effects in flexoelectric materials

Computer Methods in Applied Mechanics and Engineering

Dingle M., Arias I., Codony D. (2025)

In this work, we present a model that successfully integrates flexoelectricity and the effects of surfaces, and we properly derive the governing equations and boundary conditions for the boundary value problem. We also present a numerical approach in order to computationally solve it, ...

17

Flexoelectricity causes surface piezoelectric-like effects in dielectrics

International Journal of Mechanical Sciences

Mohammadi H., Greco F., Codony D., Arias I. (2025)

In this paper we study the surface effects that bulk flexoelectric models in finite samples exhibit. We first show that when the body is infinite, flexoelectric materials do not exhibit electromechanical response under homogeneous loading. However, when the size of the body is finite, ...

16

A comparison of formulations and non-linear solvers for computational modeling of semiconductor devices

Computational Mechanics

Pérez-Escudero S., Codony D., Arias I., Fernández-Méndez S. (2024)

The drift-diffusion formulation, modeling semiconductor materials in terms of carrier densities and electric potential, is considered together with an alternative formulation in terms of dimensionless logarithmic quantities. Stability of both formulations in presence of sharp variations ...

15

Computational homogenization of higher-order electro-mechanical materials with built-in generalized periodicity conditions

Computer Methods in Applied Mechanics and Engineering

Barceló-Mercader J., Codony D., Mocci A., Arias I. (2024)

We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying periodic architected metamaterials. Such theory ...

14

Topology optimization of flexoelectric metamaterials with apparent piezoelectricity

Journal of Mechanics and Physics of Solids

Greco F., Codony D., Mohammadi H., Fernández-Méndez S., Arias I. (2024)

We develop a theoretical and computational framework to perform topology optimization of the representative volume element of such metamaterials by accurately modeling the governing equations of flexoelectricity using a Cartesian B-spline method, describing ...

13

A note on transversal flexoelectricity in two-dimensional systems

ArXiv Preprints

Codony D., Arias I., Suryanarayana P. (2023)

In a recent letter [Phys. Rev. Lett. 127, 216801 (2021)], the authors introduced the effective flexoelectric coefficient µ2D for quantifying the flexoelectric effect in 2D materials systems, and reported a disagreement with the flexoelectric coefficient µT introduced in ...

12

Towards understanding flexoelectricity at the nanoscale

ECCOMAS Newsletter 2023

Codony D., Suryanarayana P., Arias I. (2023)

We review the authors' recent works on flexoelectricity at the nanoscale, while emphasizing the role of continuum mechanics in interpreting the electromechanical response of quantum mechanical systems under bending.

11

C0-IPM with generalised periodicity and application to flexoelectricity-based 2D metamaterials

Journal of Scientific Computing

Balcells-Quintana O., Codony D., Fernández-Méndez S. (2022)

We propose a methodology to solve high-order PDE boundary value problems with generalised periodicity, in the framework of the C0 interior penalty method. The method is developed for the analysis of flexoelectricity-based metamaterial unit cells, formalising ...

10

Weak enforcement of interface continuity and generalized periodicity in high-order electromechanical problems

International Journal of Numerical Methods in Engineering

Barceló-Mercader J., Codony D., Fernández-Méndez S., Arias I. (2022)

We present a formulation for the weak enforcement of continuity conditions at material interfaces in high-order problems by means of Nitsche's method, which is particularly suited for unfitted discretizations. This formulation is extended to impose ...

09

Mathematical and computational modeling of flexoelectricity (EP)

Journal of Applied Physics

Codony D., Mocci A., Barceló-Mercader J., Arias I. (2021)

We first revisit the mathematical modeling of the flexoelectric effect in the context of continuum mechanics at infinitesimal deformations. We establish and clarify the relation between the different formulations, point out theoretical and numerical issues ...

08

Geometrically polarized architected dielectrics with apparent piezoelectricity

Journal of the Mechanics of Physics and Solids

Mocci A., Barceló-Mercader J., Codony D., Arias I. (2021)

Through the suitable geometry of a repeating unit, a metamaterial can exhibit a property not present in the base material. Here, we propose a class of low area-fraction, bending-dominated metamaterials that exhibit apparent piezoelectricity, even ...

07

A C0 Interior Penalty Finite Element Method for Flexoelectricity

Journal of Scientific Computing

Ventura A., Codony D., Fernández-Méndez S. (2021)

We propose a C0 interior penalty method (C0-IPM) for the computational modelling of flexoelectricity, with application also to strain gradient elasticity, as a simplified case. Standard high-order C0 finite element approximations, with nodal basis, ...

06

Transversal flexoelectric coefficient for nanostructures at finite deformations from first principles

Physical Review Materials

Codony D., Arias I., Suryanarayana P. (2021)

We present a formulation for calculating the transversal flexoelectric coefficient of nanostructures at finite deformations from first principles. Specifically, we introduce the concept of radial polarization to make the coefficient a well-defined quantity for uniform bending deformations. We ...

05

Flexoelectricity in atomic monolayers from first principles

Kumar S., Codony D., Arias I., Suryanarayana P. (2021)

We study the flexoelectric effect in fifty-four select atomic monolayers using ab initio Density Functional Theory (DFT). Specifically, considering representative materials from each of the Group III monochalcogenides, transition metal dichalcogenides (TMDs), Groups IV, III–V, and V ...

04

Modeling flexoelectricity in soft dielectrics at finite deformation

Journal of the Mechanics of Physics and Solids

Codony D., Gupta P., Marco O., Arias I. (2021)

This paper develops the equilibrium equations describing the flexoelectric effect in soft dielectrics under large deformations. Previous works have developed related theories using a flexoelectric coupling tensor of mixed material–spatial character. Here, we formulate the model in terms of a ...

03

A C0 interior penalty method for 4th order PDEs

Fojo D., Codony D., Fernández Méndez S. (2020)

A method to solve 4th-order PDEs using the Finite Element Method (FEM) with standard Cº elements is derived and studied. It is based on a special weak form accounting for the discontinuous derivatives of the approximation and imposing their normal continuity across element sides in weak form. ...

02

An immersed boundary hierarchical B-spline method for flexoelectricity

Computer Methods in Applied Mechanics and Engineering

Codony D., Marco O., Arias I., Fernández Méndez S. (2019)

This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order nature of the coupled PDE system is addressed by a sufficiently ...

01

From physical to digital in structural engineering classrooms using digital fabrication

Computer Applications in Engineering Education

Chacón R., Codony D., Toledo Á. (2017)

In this paper, a set of digital artifacts related to simple examples of structural engineering are presented. The artifacts are real-time applications and visualizations of typical problems students from the architecture, engineering, and construction (AEC) schools are acquainted with. The ...

TH

Mathematical and computational modeling of flexoelectricity at mesoscopic and atomistic scales

Doctoral thesis - Universitat Politècnica de Catalunya

Codony D. (2021)

This PhD thesis focuses on the development of mathematical and computational models for flexoelectricity, a relatively new electromechanical coupling that is present in any dielectric at the micron and sub-micron scales. The work is framed in the context of both continuum and quantum...

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