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2023 | OriginalPaper | Chapter

Alternative Crack-Tip Enrichment Functions for X-FEM in Arbitrary Polarized Piezoelectric Media

Authors : Rajalaxmi Rath, Kuldeep Sharma

Published in: Frontiers in Industrial and Applied Mathematics

Publisher: Springer Nature Singapore

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Abstract

In this paper, a new approach is proposed to study the fracture mechanics problems in 2-D arbitrary polarized piezoelectric media using X-FEM. The existing six-fold crack-tip enrichment functions defined for the generalized case of poling and alignment of crack in piezoelectric media are re-defined here by considering the localized solution of crack-tip field based on Lekhnitskii’s formalism in the transformed coordinate system obtained from material axes to crack-axes, whereas the existing crack-tip enrichment functions were developed other way round. Using the proposed enrichment functions, some benchmark problems such as center cracks, edge cracks, double-edge cracks, and macro–micro-collinear cracks have been studied under arbitrary poling direction, plain strain, and impermeable crack-face conditions. An excellent agreement of normalized intensity factors (IFs) has been obtained for all the cases with the results of existing six-fold enrichment functions.

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previous chapter On the Existence and Stability Analysis for -Caputo Fractional Boundary Value Poblem
next chapter Convergence Analysis of a Layer Resolving Numerical Techniquefor a Class of Coupled System of Singularly Perturbed Parabolic Convection-Diffusion Equations Having an Interface
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Sharma, K., Bui, T.Q., Singh, S.: Numerical distributed dislocation modeling of multiple cracks in piezoelectric media considering different crack-face boundary conditions and finite size effects. Strength. Fract. Complex. 10, 49–72 (2017)CrossRef
Metadata
Title
Alternative Crack-Tip Enrichment Functions for X-FEM in Arbitrary Polarized Piezoelectric Media
Authors
Rajalaxmi Rath
Kuldeep Sharma
Copyright Year
2023
Publisher
Springer Nature Singapore
Book
Frontiers in Industrial and Applied Mathematics

Print ISBN: 978-981-19-7271-3

Electronic ISBN: 978-981-19-7272-0

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-981-19-7272-0_19

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