Vol. 16, No. 2, 2021

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A new meshless Fragile Points Method (FPM) with minimum unknowns at each point, for flexoelectric analysis under two theories with crack propagation, II: Validation and discussion

Yue Guan, Leiting Dong and Satya N. Atluri

Vol. 16 (2021), No. 2, 197–223

In the first part of this two-paper series, a new Fragile Points Method (FPM), in both primal and mixed formulations, is presented for analyzing flexoelectric effects in 2D dielectric materials. In the present paper, a number of numerical results are provided as validations, including linear and quadratic patch tests, flexoelectric effects in continuous domains, and analyses of stationary cracks in dielectric materials. A discussion of the influence of the electroelastic stress is also given, showing that Maxwell stress could be significant and thus the full flexoelectric theory is recommended to be employed for nanoscale structures. The present primal as well as mixed FPMs also show their suitability and effectiveness in simulating crack initiation and propagation with flexoelectric effect. Flexoelectricity, coupled with piezoelectric effect, can help, hinder, or deflect the crack propagation paths and should not be neglected in nanoscale crack analysis. In FPM, no remeshing or trial function enhancement are required in modeling crack propagation. A new Bonding-Energy-Rate (BER)-based crack criterion as well as classic stress-based criterion are used for crack development simulations.

flexoelectricity, strain gradient effect, fragile points method (FPM), crack propagation
Received: 27 September 2020
Accepted: 22 January 2021
Published: 6 June 2021
Yue Guan
Department of Mechanical Engineering
Texas Tech University
Lubbock, TX
United States
Leiting Dong
School of Aeronautic Science and Engineering
Beihang University
Satya N. Atluri
Department of Mechanical Engineering
Texas Tech University
Lubbock, TX
United States