Non-local theory solution for a plane rectangular crack in a 3D infinite transversely isotropic elastic material under a time-harmonic elastic P-wave

2014 ◽  
Vol 47 ◽  
pp. 327-340 ◽  
Author(s):  
Hai-Tao Liu ◽  
Zhen-Gong Zhou
Keyword(s):  
Elastic Material ◽  
Transversely Isotropic ◽  
P Wave ◽  
Local Theory ◽  
Rectangular Crack ◽  
Isotropic Elastic Material ◽  
Time Harmonic ◽  
Non Local ◽  
Theory Solution

Fundamental solutions of two 3D rectangular semi-permeable cracks in transversely isotropic piezoelectric media based on the non-local theory

2020 ◽  
Vol 16 (6) ◽  
pp. 1497-1520
Author(s):  
Haitao Liu ◽  
Liang Wang
Keyword(s):  
Electric Displacement ◽  
Transversely Isotropic ◽  
Elastic Behavior ◽  
Classical Solutions ◽  
Local Theory ◽  
Dual Integral Equations ◽  
Piezoelectric Media ◽  
Content Type ◽  
Present Solution ◽  
Non Local

PurposeThe paper aims to present the non-local theory solution of two three-dimensional (3D) rectangular semi-permeable cracks in transversely isotropic piezoelectric media under a normal stress loading.Design/methodology/approachThe fracture problem is solved by using the non-local theory, the generalized Almansi's theorem and the Schmidt method. By Fourier transform, this problem is formulated as three pairs of dual integral equations, in which the elastic and electric displacements jump across the crack surfaces. Finally, the non-local stress and the non-local electric displacement fields near the crack edges in piezoelectric media are derived.FindingsDifferent from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack edges in piezoelectric media.Originality/valueAccording to the literature survey, the electro-elastic behavior of two 3D rectangular cracks in piezoelectric media under the semi-permeable boundary conditions has not been reported by means of the non-local theory so far.

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