Formulation for Multiple Cracks Problem in Thermoelectric-Bonded Materials Using Hypersingular Integral Equations

Muhammad Haziq Iqmal Mohd Nordin, Khairum Bin Hamzah (), Najiyah Safwa Khashi’ie, Iskandar Waini, Nik Mohd Asri Nik Long and Saadatul Fitri
Additional contact information
Muhammad Haziq Iqmal Mohd Nordin: Fakulti Kejuruteraan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal 76100, Melaka, Malaysia
Khairum Bin Hamzah: Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal 76100, Melaka, Malaysia
Najiyah Safwa Khashi’ie: Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal 76100, Melaka, Malaysia
Iskandar Waini: Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal 76100, Melaka, Malaysia
Nik Mohd Asri Nik Long: Mathematics Department, Faculty of Science, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
Saadatul Fitri: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Malang 65145, Indonesia

Mathematics, 2023, vol. 11, issue 14, 1-20

Abstract: New formulations are produced for problems associated with multiple cracks in the upper part of thermoelectric-bonded materials subjected to remote stress using hypersingular integral equations (HSIEs). The modified complex stress potential function method with the continuity conditions of the resultant electric force and displacement electric function, and temperature and resultant heat flux being continuous across the bonded materials’ interface, is used to develop these HSIEs. The unknown crack opening displacement function, electric current density, and energy flux load are mapped into the square root singularity function using the curved length coordinate method. The new HSIEs for multiple cracks in the upper part of thermoelectric-bonded materials can be obtained by applying the superposition principle. The appropriate quadrature formulas are then used to find stress intensity factors, with the traction along the crack as the right-hand term with the help of the curved length coordinate method. The general solutions of HSIEs for crack problems in thermoelectric-bonded materials are demonstrated with two substitutions and it is strictly confirmed with rigorous proof that: (i) the general solutions of HSIEs reduce to infinite materials if G 1 = G 2 , K 1 = K 2 , and E 1 = E 2 , and the values of the electric parts are α 1 = α 2 = 0 and λ 1 = λ 2 = 0 ; (ii) the general solutions of HSIEs reduce to half-plane materials if G 2 = 0 , and the values of α 1 = α 2 = 0 , λ 1 = λ 2 = 0 and κ 2 = 0 . These substitutions also partially validate the general solution derived from this study.

Keywords: multiple cracks; thermoelectric; bonded materials; hypersingular integral equations; modified complex stress potential (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/14/3248/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/14/3248/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:14:p:3248-:d:1201353

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().