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Two equal collinear cracks in magneto-electro-elastic materials: A study of electric and magnetic poling influences

   | Jun 26, 2020

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Fig. 1

Schematic representation of the problem
Schematic representation of the problem

Fig. 2

SIF versus inter-crack distance for different electric poling with fixed magnetic poling
SIF versus inter-crack distance for different electric poling with fixed magnetic poling

Fig. 3

SIF versus inter-crack distance for different electric poling with fixed magnetic poling
SIF versus inter-crack distance for different electric poling with fixed magnetic poling

Fig. 4

SIF versus inter-crack distance for different electric poling with fixed magnetic poling
SIF versus inter-crack distance for different electric poling with fixed magnetic poling

Fig. 5

EDIF versus inter-crack distance for different electric poling with fixed magnetic poling
EDIF versus inter-crack distance for different electric poling with fixed magnetic poling

Fig. 6

EDIF versus inter-crack distance for different electric poling with fixed magnetic poling
EDIF versus inter-crack distance for different electric poling with fixed magnetic poling

Fig. 7

EDIF versus inter-crack distance for different electric poling with fixed magnetic poling
EDIF versus inter-crack distance for different electric poling with fixed magnetic poling

Fig. 8

MIIF versus inter-crack distance for different electric poling with fixed magnetic poling
MIIF versus inter-crack distance for different electric poling with fixed magnetic poling

Fig. 9

MIIF versus inter-crack distance for different electric poling with fixed magnetic poling
MIIF versus inter-crack distance for different electric poling with fixed magnetic poling

Fig. 10

MIIF versus inter-crack distance for different electric poling with fixed magnetic poling
MIIF versus inter-crack distance for different electric poling with fixed magnetic poling

Fig. 11

SIF versus inter-crack distance for different magnetic poling with fixed electric poling
SIF versus inter-crack distance for different magnetic poling with fixed electric poling

Fig. 12

SIF versus inter-crack distance for different magnetic poling with fixed electric poling
SIF versus inter-crack distance for different magnetic poling with fixed electric poling

Fig. 13

SIF versus inter-crack distance for different magnetic poling with fixed electric poling
SIF versus inter-crack distance for different magnetic poling with fixed electric poling

Fig. 14

EDIF versus inter-crack distance for different magnetic poling with fixed electric poling
EDIF versus inter-crack distance for different magnetic poling with fixed electric poling

Fig. 15

EDIF versus inter-crack distance for different magnetic poling with fixed electric poling
EDIF versus inter-crack distance for different magnetic poling with fixed electric poling

Fig. 16

EDIF versus inter-crack distance for different magnetic poling with fixed electric poling
EDIF versus inter-crack distance for different magnetic poling with fixed electric poling

Fig. 17

MIIF versus inter-crack distance for different magnetic poling with fixed electric poling
MIIF versus inter-crack distance for different magnetic poling with fixed electric poling

Fig. 18

MIIF versus inter-crack distance for different magnetic poling with fixed electric poling
MIIF versus inter-crack distance for different magnetic poling with fixed electric poling

Fig. 19

MIIF versus inter-crack distance for different magnetic poling with fixed electric poling
MIIF versus inter-crack distance for different magnetic poling with fixed electric poling

Symbol Notation
d inner crack tip
c outer crack tip
eiks piezoelectric constants
f analytic function
hiks piezomagnetic constants
k1 elliptic modulus
mE coordinate transfer matrix of electric poling
mH coordinate transfer matrix of magnetic poling
u generalized displacement vector
ui (i = 1,2,3) mechanical displacement
xi (i = 1,2,3) material coordinate system
z complex variable
Cijks elastic constants
E(k1) complete elliptic integral of second kind
F(k1) complete elliptic integral of first kind
MB material constants transform matrix of the inclusion
MC material constants transform matrix of the matrix
Vf volume fraction of the inclusion
αis dielectric permittivities
βis electromagnetic constants
γis magnetic permeabilities
u4 = ϕ electric potential
u5 = φ magnetic potential
χ Jacobi amplitude
eISSN:
2444-8656
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics