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# Three-Dimensional Isogeometric Analysis of Flexoelectricity with MATLAB Implementation

Hamid Ghasemi1, Harold S. Park2, Xiaoying Zhuang3, 4, *, Timon Rabczuk5, 6

1 Department of Mechanical Engineering, Arak University of Technology, Arak, 38181-41167, Iran.
2 Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA.
3 Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
4 Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
5 Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia.
6 Institute of Structural Mechanics, Bauhaus-Universität Weimar, Weimar, D-99423, Germany.

* Corresponding Author: Xiaoying Zhuang. Email: .

Computers, Materials & Continua 2020, 65(2), 1157-1179. https://doi.org/10.32604/cmc.2020.08358

## Abstract

Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa. The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect. We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup. Besides educational purposes, this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy. The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods community to learn how to solve a fully coupled problem, which requires higher order approximations, numerically. The complete MATLAB code which is available as source code distributed under a BSD-style license, is provided in the part of Supplementary Materials of the paper.

## Keywords

H. Ghasemi, H. S. Park, X. Zhuang and T. Rabczuk, "Three-dimensional isogeometric analysis of flexoelectricity with matlab implementation," Computers, Materials & Continua, vol. 65, no.2, pp. 1157–1179, 2020.

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