A New Meshless Fragile Points Method (FPM) With Minimum Unknowns at Each Point, For Flexoelectric Analysis Under Two Theories with Crack Propagation. Part II: Validation and discussion

TL;DR

This paper validates a novel meshless Fragile Points Method for analyzing flexoelectric effects and crack propagation in nano-scale dielectric materials, emphasizing the importance of full electroelastic stress considerations.

Contribution

It introduces and validates a new FPM approach for flexoelectric analysis that effectively models crack initiation and growth without remeshing, incorporating full electroelastic stress effects.

Findings

Full flexoelectric theory is recommended for nano-scale structures.

FPM accurately simulates crack initiation and propagation.

Flexoelectric effects influence crack paths significantly.

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 nano-scale 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 nano-scale 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. Other complex problems such as dynamic crack developments, fracture, fragmentation and 3D flexoelectric analyses will be given in our future studies.