Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T20:51:15.570Z Has data issue: false hasContentIssue false
  • English
  • Français

Cracks Interaction in a Pre-Stressed and Pre-Polarized Piezoelectric Material

Published online by Cambridge University Press:  17 January 2020

E.M. Craciun ,
A. Rabaea  and
S. Das
E.M. Craciun*
Affiliation:
Department of Naval, Port and Power Engineering, “Ovidius” University of Constanta, Constanta, Romania
A. Rabaea
Affiliation:
Department of Mathematics and Computer Science, Technical University of Cluj-Napoca, N.U.C.B.M. Baia Mare, Romania
S. Das
Affiliation:
Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi-221005, India
*
* Corresponding author ([email protected])
Get access

Abstract

We formulate and solve the mathematical problem for antiplane cracks in a pre-stressed and pre-polarized piezoelectric material with static initial fields, assuming the initially deformed configuration of the body is locally stable. Using the boundary conditions of antiplane cracks, we get the Riemann-Hilbert problems. Nonhomogeneous linear complex differential equations having the unknown complex potential are obtained. For constant value of the applied incremental forces can be obtained the complex potentials, incremental displacement and stress fields corresponding to the third mode of the classical fracture. The problem of interaction of two collinear, unequal cracks in a pre-stressed and pre-polarized piezoelectric material, is also studied.

Keywords

piezoelectricitypre-stressedpre-polarizedcracks interactionantiplane mode
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 2 , April 2020 , pp. 177 - 182
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Sosa, H., “On the fracture mechanics of piezoelectric solids,” International Journal of Solids Structures, 29(21), pp. 2613–2622 (1992).CrossRefGoogle Scholar
Sosa, H., Khutoryansky, N., “New developments concerning piezoelectric materials with defects,” International Journal of Solids Structures, 33, pp. 3399–3414 (1996).CrossRefGoogle Scholar
Pak, Y.E., “Crack extension force in a piezoelectric material,” Journal of Applied Mechanics, 57(3), pp. 647–653 (1990).CrossRefGoogle Scholar
Pak, Y.E, “Linear electro-elastic fracture mechanics of piezoelectric materials,” International Journal of Fracture, 54, pp.79–100 (1992).CrossRefGoogle Scholar
Soos, E., “Stability, resonance and stress concentration in prestressed piezoelectric crystals containing a crack,” International Journal of Engineering Science, 34(14), pp. 1647–1673 (1996).CrossRefGoogle Scholar
Cristescu, N., Craciun, E.M. and Soos, E., Mechanics of Elastic Composites, CRC Press, Chapman and Hall, Boca Raton, FL. (2004).Google Scholar
Craciun, E.M., Baesu, E. and Soos, E., “General solution in terms of complex potentials in antiplane states in prestressed and prepolarized piezoelectric crystals: application to Mode III fracture propagation,” IMA Journal of Applied Mathematics, 70, pp. 39–52 (2005).CrossRefGoogle Scholar
Baesu, E., Soos, E., “Antiplane piezoelectricity in the presence of initial mechanical and electric fields,” Mathematics and Mechanics of Solids, 6, pp. 409–422 (2001).CrossRefGoogle Scholar
Baesu, E., Soos, E. “Antiplane fracture in a prestressed and prepolarized crystal,” IMA Journal of Applied Mathematics, 66, pp. 499–508 (2001).CrossRefGoogle Scholar
Baesu, E., Fortune, D. and Soos, E. “Incremental behaviour of hyperelastic dielectrics and piezoelectric crystals,” Journal of Applied Mathematics and Physics (ZAMP), 54, pp. 160–178 (2003).CrossRefGoogle Scholar
Craciun, E.M., Soos, E. “Interaction of two unequal cracks in a prestressed fiber reinforced elastic composite,” International Journal of Fracture 94, pp. 137–159 (1996).CrossRefGoogle Scholar
Das, S. “Interaction of moving interface collinear Griffith cracks under antiplane shear,” International Journal of Solids Structures, 43, pp. 7880–7890 (2006).CrossRefGoogle Scholar
Sadowski, T., Craciun, E.M., Rabaea, A. and Marsavina, L. “Mathematical modeling of three equal collinear cracks in an orthotropic solid,” Meccanica, 51(2), pp. 329–339 (2016).CrossRefGoogle Scholar