Skip to main content Accessibility help
×
Home
Hostname: page-component-684bc48f8b-9ddkh Total loading time: 0.183 Render date: 2021-04-12T00:04:46.426Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

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

Published online by Cambridge University Press:  17 January 2020

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
E-mail address:
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.

Type
Research Article
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.

References

Sosa, H., “On the fracture mechanics of piezoelectric solids,” International Journal of Solids Structures, 29(21), pp. 26132622 (1992).CrossRefGoogle Scholar
Sosa, H., Khutoryansky, N., “New developments concerning piezoelectric materials with defects,” International Journal of Solids Structures, 33, pp. 33993414 (1996).CrossRefGoogle Scholar
Pak, Y.E., “Crack extension force in a piezoelectric material,” Journal of Applied Mechanics, 57(3), pp. 647653 (1990).CrossRefGoogle Scholar
Pak, Y.E, “Linear electro-elastic fracture mechanics of piezoelectric materials,” International Journal of Fracture, 54, pp.79100 (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. 16471673 (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. 3952 (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. 409422 (2001).CrossRefGoogle Scholar
Baesu, E., Soos, E.Antiplane fracture in a prestressed and prepolarized crystal,” IMA Journal of Applied Mathematics, 66, pp. 499508 (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. 160178 (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. 137159 (1996).CrossRefGoogle Scholar
Das, S.Interaction of moving interface collinear Griffith cracks under antiplane shear,” International Journal of Solids Structures, 43, pp. 78807890 (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. 329339 (2016).CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 54 *
View data table for this chart

* Views captured on Cambridge Core between 17th January 2020 - 12th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Cracks Interaction in a Pre-Stressed and Pre-Polarized Piezoelectric Material
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Cracks Interaction in a Pre-Stressed and Pre-Polarized Piezoelectric Material
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Cracks Interaction in a Pre-Stressed and Pre-Polarized Piezoelectric Material
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *