scholarly journals Higher Order Mechanical and Electric Fields for Arbitrarily Oriented Crack with the Physical Weak-Discontinuity

Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Yumeng Shi ◽  
Jincai Huang
2011 ◽  
Vol 217-218 ◽  
pp. 1314-1318
Author(s):  
Yao Dai ◽  
Lei Zhang ◽  
Peng Zhang ◽  
Jun Feng Liu

The higher order discontinuous asymptotic fields which are similar to the Williams’ solutions of homogenous material are obtained by the displacement method and asymptotic analysis for a plane crack at the physical weak-discontinuous interface in non-homogeneous materials. The results provide a theoretical basis for the numerical analysis, experimental investigation and the engineering application of physical weak-discontinuous fracture.


2010 ◽  
Vol 28 (9) ◽  
pp. 1777-1794 ◽  
Author(s):  
R. Cosgrove ◽  
R. Doe

Abstract. The ionospheric feedback instability (IFI), which involves feedback between ionospheric modifications and waves reflected off the magnetosphere, has up to this point been analyzed in terms of field line integrated (FLI) ionospheric quantities, that is, with the assumption that the ionospheric thickness can be ignored. In this work we test this assumption by solving the two-fluid equations for a representative ionospheric slab of finite thickness. We find that the results are for the most part incompatible with a description in terms of FLI quantities, and that their use can easily lead to an order of magnitude overestimation of the growth rate. This occurs because the first eigenmode, which is the one compatible with an FLI description, is cutoff above a certain frequency, leaving only higher order modes with wavelengths along B that are subsumed by the slab. Taking the results at face value, the parallel electric fields associated with the higher order modes are a possible contributor to electron heating and plasma structure in the E-region ionosphere.


2014 ◽  
Vol 602-605 ◽  
pp. 283-286
Author(s):  
Yao Dai ◽  
Xiao Chong

The higher order crack-tip fields for anti-plane crack oblique to the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The crack is oriented in arbitrary direction. The crack surfaces are assumed to be electrically impermeable. The material properties of FGPMs are assumed to be linear functions with their gradient direction perpendicular to the interface. By using the eigen-expansion method, the high order crack tip stress and electric displacement fields are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.


2011 ◽  
Vol 217-218 ◽  
pp. 1309-1313
Author(s):  
Yao Dai ◽  
Shi Min Li ◽  
Peng Zhang ◽  
Xiao Chong

An arbitrarily oriented anti-plane crack with its tip at the physical weak-discontinuous line of the structure which is made up of homogeneous material and functionally graded materials (FGMs) is studied. The analytic solution of the higher order crack tip fields (similar to the Williams’ solution of homogenous material) is obtained by applying the asymptotic series expansion. When non-homogeneous material parameters are degenerated, the solutions become the same as the asymptotic crack tip fields of the homogeneous material. Therefore, the solutions are the basic results of non-homogeneous fracture mechanics, and provide a theoretical basis for solving the fracture problems of one common structure with physical weak-discontinuity.


Physics ◽  
2019 ◽  
Vol 1 (3) ◽  
pp. 392-401 ◽  
Author(s):  
Nathaniel K. Hicks ◽  
Amanda Bowman ◽  
Katarina Godden

Radio-frequency (RF) charged particle traps, such as the Paul trap or higher order RF multipole traps, may be used to trap quasi-neutral plasma. The presence of positive and negative plasma species mitigates the ejection of particles that occurs due to space charge repulsion. For symmetric species, such as a pair plasma, the trapped particle distribution is essentially equal for both species. For plasma with species of disparate charge-to-mass ratio, the RF parameters are chosen to directly trap the lighter species, leading to loss of the heavier species until sufficient net space charge develops to prevent further loss. Two-dimensional (2D) electrostatic particle-in-cell simulations are performed of cases with mass ratio m+/m− = 10, and also with ion–electron plasma. Multipole cases including order N = 2 (quadrupole) and higher order N = 8 (hexadecapole) are considered. The light ion-heavy ion N = 8 case exhibits particles losses less than 5% over 2500 RF periods, but the N = 8 ion–electron case exhibits a higher loss rate, likely due to non-adiabaticity of electron trajectories at the boundary, but still with low total electron loss current on the order of 10 μA. The N = 2 ion-electron case is adiabatic and stable, but is subject to a smaller trapping volume and greater initial perturbation of the bulk plasma by the trapping field.


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