Fracture Mechanics Analysis of Piezoelectric Materials Using an Efficient Collocation Element Differential Method

authored by: Jun Lv, Yi Yang, Miao Cui, Huayu Liu, Bingbing Xu, Xiaowei Gao
Abstract: This paper presents a novel element differential method for modeling cracks in piezoelectric materials, aiming to simulate fracture behaviors and predict the fracture parameter known as the J-integral accurately. The method leverages an efficient collocation technique to satisfy traction and electric charge equilibrium on the crack surface, aligning internal nodes with piezoelectric governing equations without needing integration or variational principles. It combines the strengths of the strong form collocation and finite element methods. The J-integral is derived analytically using the equivalent domain integral method, employing Green's formula and Gauss's divergence theorem to transform line integrals into area integrals for solving two-dimensional piezoelectric material problems. The accuracy of the method is validated through comparison with three typical examples, and it offers fracture prevention strategies for engineering piezoelectric structures under different electrical loading patterns.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Dalian University of Technology
Type: Article
Journal: Acta mechanica solida Sinica
No. of pages: 12
ISSN: 0894-9166
Publication date: 03.01.2025
Publication status: E-pub ahead of print
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering
Electronic version(s): https://doi.org/10.1007/s10338-024-00566-5 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{fe831f3a34264f74af91ca7ca6cfcd86,
title = "Fracture Mechanics Analysis of Piezoelectric Materials Using an Efficient Collocation Element Differential Method",
abstract = "This paper presents a novel element differential method for modeling cracks in piezoelectric materials, aiming to simulate fracture behaviors and predict the fracture parameter known as the J-integral accurately. The method leverages an efficient collocation technique to satisfy traction and electric charge equilibrium on the crack surface, aligning internal nodes with piezoelectric governing equations without needing integration or variational principles. It combines the strengths of the strong form collocation and finite element methods. The J-integral is derived analytically using the equivalent domain integral method, employing Green's formula and Gauss's divergence theorem to transform line integrals into area integrals for solving two-dimensional piezoelectric material problems. The accuracy of the method is validated through comparison with three typical examples, and it offers fracture prevention strategies for engineering piezoelectric structures under different electrical loading patterns.",
keywords = "Electro-mechanical coupling, Element differential method, Fracture mechanics, J-integral",
author = "Jun Lv and Yi Yang and Miao Cui and Huayu Liu and Bingbing Xu and Xiaowei Gao",
note = "Publisher Copyright: {\textcopyright} The Chinese Society of Theoretical and Applied Mechanics 2025.",
year = "2025",
month = jan,
day = "3",
doi = "10.1007/s10338-024-00566-5",
language = "English",
journal = "Acta mechanica solida Sinica",
issn = "0894-9166",
publisher = "Huazhong University of Science and Technology",
}