By Petia Dineva

ISBN-10: 3319039601

ISBN-13: 9783319039602

ISBN-10: 331903961X

ISBN-13: 9783319039619

*Dynamic Fracture of Piezoelectric Materials* specializes in the Boundary fundamental Equation process as an effective computational device. The presentation of the theoretical foundation of piezoelectricity is through sections on basic recommendations and the numerical attention of the boundary worth difficulties. significant elements of the ebook are dedicated to the answer of difficulties in homogeneous and inhomogeneous solids. The ebook comprises contributions on coupled electro-mechanical versions, computational tools, its validation and the simulation effects, which display diverse results invaluable for engineering layout and perform. The booklet is self-contained and well-illustrated, and it serves as a graduate-level textbook or as additional interpreting fabric for college students and researchers.

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**Example text**

40) it is obvious that uˆ ∓43 = uˆ ∓34 . It remains to solve the equation for uˆ ∓44 . From Eq. 38) we have e15 Φs2 uˆ ∓34 − ε11 Φs2 uˆ ∓44 = −χ(s − θ ), and using Eq. 40) we get the equation Φs2 uˆ ∓44 = − 2 k ie15 2 a 2ε11 0 ⎪ eik|s−θ | + e2 1 − 2 15 ε11 ε11 a0 ⎨ χ(s − θ ). 41) Solving Eq. 40), we finally obtain uˆ ∓44 = 2 e15 2 ε11 uˆ ∓33 + 1 |s − θ |. 3 Anti-plane Piezoelectric Case u ∓33 (x, α ) = 47 1 8σ 2 a0 |m|=1 {iσ eikπ − 2[ci(kπ) cos(kπ) + si(kπ) sin(kπ)]}|π=| x−α,m√| dm, 2 e15 u ∓ (x, α ), ε11 33 e2 ∓ 1 u ∓44 (x, α ) = 15 u 33 (x, α ) + ln |x − α |.

McMeeking RM (2004) The energy release rate for a Griffith crack in a piezoelectric material. Eng Fract Mech 71:1149–1163 26. Newnham RE (1980) Composite piezoelectric transducers. Mater Eng 2:93–106 27. Pak YE (1992b) Linear electro-elastic fracture mechanics of piezoelectric materials. Int J Fract 54:79–100 28. Park SB, Sun CT (1995) Effect of electric field on fracture of piezoelectric ceramics. Int J Fract 70(3):203–216 29. Parton VZ, Kudryavtsev BA (1988) Electromagnetoelasticity. Gordon and Breach Science, New York 30.

49 has the form C(m) = (λ + 2μ)m 21 + μm 22 (λ + μ)m 1 m 2 . 66) In this case the eigenvalues ai of matrix C(m) defined in Eq. 50) do not depend λ + 2μ, a2 = μ, the on m, a1 = ⎛ ⎛ eigenvectors are g1 = (m 1 , −m 2 ), g2 = (m 2 , m 1 ) ρ ρ , k2 = ω . 69) s=| x−α,m√| m p sign x − α, m√dm.

### Dynamic Fracture of Piezoelectric Materials: Solution of Time-Harmonic Problems via BIEM by Petia Dineva

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