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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 |
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Vol. 16 (2021), No. 2, 197–223
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Abstract |
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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. |
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Keywords
flexoelectricity, strain gradient effect, fragile points
method (FPM), crack propagation
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Milestones
Received: 27 September 2020
Accepted: 22 January 2021
Published: 6 June 2021
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Authors |
| Yue Guan | |
| Department of Mechanical
Engineering Texas Tech University Lubbock, TX United States |
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| Leiting Dong | |
| School of Aeronautic Science and
Engineering Beihang University Beijing China |
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| Satya N. Atluri | |
| Department of Mechanical
Engineering Texas Tech University Lubbock, TX United States |
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