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Riemann–Hilbert approach-based analytical solutions for strip saturated two unequal collinear cracks in piezoelectric media

Riemann–Hilbert approach-based analytical solutions for strip saturated two unequal collinear... The objective of the work is to derive analytical solutions based on the Riemann–Hilbert (R–H) approach for semipermeable strip saturated two unequal collinear cracks in arbitrary polarized piezoelectric media. We particularly consider the influence of far field electromechanical loadings, poling direction and different crack-face boundary conditions. The problem is mathematically formulated into a set of non-homogeneous R–H problems in terms of complex potential functions (related to field components) using complex variable and extended Stroh formalism approach. After solving these equations, explicit solutions are obtained for the involved unknown complex potential functions and hence, the stress and electric displacement components at any point within the domain. Furthermore, after employing standard limiting conditions, explicit expressions for some conventional fracture parameters such as saturated zone lengths (in terms of nonlinear equations), local stress intensity factors and crack opening displacement are obtained. Numerical studies are presented for the PZT-4H material to analyze the effects of prescribed electromechanical loadings, inter-cracks distance, crack-face conditions and poling direction on the defined fracture parameters. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Strength, Fracture and Complexity IOS Press

Riemann–Hilbert approach-based analytical solutions for strip saturated two unequal collinear cracks in piezoelectric media

Singh, Sandeep; Sharma, Kuldeep
Strength, Fracture and Complexity , Volume 13 (4): 19 – Apr 27, 2021
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Publisher
IOS Press
Copyright
Copyright © 2021 © 2021 – IOS Press. All rights reserved
ISSN
1567-2069
eISSN
1875-9262
DOI
10.3233/SFC-200261
Publisher site
See Article on Publisher Site

Abstract

The objective of the work is to derive analytical solutions based on the Riemann–Hilbert (R–H) approach for semipermeable strip saturated two unequal collinear cracks in arbitrary polarized piezoelectric media. We particularly consider the influence of far field electromechanical loadings, poling direction and different crack-face boundary conditions. The problem is mathematically formulated into a set of non-homogeneous R–H problems in terms of complex potential functions (related to field components) using complex variable and extended Stroh formalism approach. After solving these equations, explicit solutions are obtained for the involved unknown complex potential functions and hence, the stress and electric displacement components at any point within the domain. Furthermore, after employing standard limiting conditions, explicit expressions for some conventional fracture parameters such as saturated zone lengths (in terms of nonlinear equations), local stress intensity factors and crack opening displacement are obtained. Numerical studies are presented for the PZT-4H material to analyze the effects of prescribed electromechanical loadings, inter-cracks distance, crack-face conditions and poling direction on the defined fracture parameters.

Journal

Strength, Fracture and Complexity – IOS Press

Published: Apr 27, 2021

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