Periodic Set of the Interface Cracks with Limited Electric Permeability

  • V. V. Loboda
  • S. V. Kozinov
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 24)


Plane problem for an infinite space which consists of two different piezoelectric materials with periodic set of the limited electrically permeable interface cracks is considered. Uniformly distributed electromechanical loading is applied. The solution of the problem is obtained in close form by use of complex function theory. Formulae for stresses, electric displacement vector, elastic displacements and electric potential jump at the interface as well as the intensity factors at the crack tips are given. The main attention is paid to the influence of electric permeability of the cracks on electromechanical fields in the composite. As a particular case the periodic set of limited permeable cracks in a homogeneous piezoelectric material is studied.


Piezoelectric Material Interface Crack Electric Displacement Permeable Crack Impermeable Crack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Deeg W (1980) The analysis of dislocation, crack and inclusion problems in piezoelectric solids. Ph.D. Thesis, Stanford UniversityGoogle Scholar
  2. 2.
    Gakhov F (1966) Boundary value problems. Pergamon Press, OxfordzbMATHGoogle Scholar
  3. 3.
    Gao C-F, Kessler H, Balke H (2003) Crack problem in magnetoelectroelastic solids. Part II: general solution of collinear cracks. Int J Eng Sci 41:983–994MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Govorukha V, Loboda V, Kamlah M (2006) On the influence of the electric permeability on an interface crack in a piezoelectric bimaterial compound. Int J Solids Struct 43:1979–1990zbMATHCrossRefGoogle Scholar
  5. 5.
    Gruebner O, Kamlah M, Munz D (2003) Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium. Eng Fract Mech. 70:1399–1413CrossRefGoogle Scholar
  6. 6.
    Hao T, Shen Z (1994) A new electric boundary condition of electric fracture mechanics and its applications. Eng Fract Mech 47:793–802CrossRefGoogle Scholar
  7. 7.
    Herrmann K, Loboda V (2000) Fracture-mechanical assessment of electrically permeable interface cracks in piezoelectric bimaterials by consideration of various contact zone models. Arch Appl Mech 70:127–143zbMATHCrossRefGoogle Scholar
  8. 8.
    Kudryavtsev B, Rakitin V (1976) Periodic set of cracks in the boundary of a piezoelectric and a rigid conductor. Isv. AN SSSR. Mechanika Tvordogo Tela 2:121–129 [in Russian]Google Scholar
  9. 9.
    Landis C (2004) Electrically consistent boundary conditions for electromechanical fracture. Int J Solids Struct 41:6291–6315zbMATHCrossRefGoogle Scholar
  10. 10.
    Li Q, Chen Y (2008) Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric bimaterials. ASME J Appl Mech 75:011010-1-13Google Scholar
  11. 11.
    Li W, McMeeking R, Landis (2008) On the crack face boundary conditions in electromechanical fracture and an experimental protocol for determining energy release rates. Eur J Mech A/Solids 27:285–301Google Scholar
  12. 12.
    McMeeking R (1999) Crack tip energy release rate for a piezoelectric compact tension specimen. Eng Fract Mech 64:217–244CrossRefGoogle Scholar
  13. 13.
    Pak Y (1992) Linear electro-elastic fracture mechanics of piezoelectric materials. Int J Fract 54:79–100CrossRefGoogle Scholar
  14. 14.
    Parton V (1976) Fracture mechanics of piezoelectric materials. Acta Astronaut 3:671–683zbMATHCrossRefGoogle Scholar
  15. 15.
    Parton V, Kudryavtsev B (1988) Electromagnetoelasticity. Gordon and Breach Science Publishers, New YorkGoogle Scholar
  16. 16.
    Ricoeur A, Kuna M (2009) Electrostatic traction at dielectric interfaces and their implication for crack boundary conditions. Mech Res Commun 36:330–335zbMATHCrossRefGoogle Scholar
  17. 17.
    Suo Z, Kuo C, Barnett D, Willis J (1992) Fracture mechanics for piezoelectric ceramics. J Mech Phys Solids 40:739–765MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Wang B, May Y (2003) On the electrical boundary conditions on the crack surfaces in piezoelectric ceramics. Int J Eng Sci 41:633–652CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Theoretical and Applied MechanicsDniepropetrovsk National UniversityDniepropetrovskUkraine

Personalised recommendations