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
Abstract
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 stressbased criterion are used for crack development simulations.
Publication Title
Journal of Mechanics of Materials and Structures
Recommended Citation
Guan, Y., Dong, L., & Atluri, S. (2021). 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. Journal of Mechanics of Materials and Structures, 16 (2), 197-223. https://doi.org/10.2140/JOMMS.2021.16.197
