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Analysis of multiple parallel cracks in a functionally graded magneto-electro-elastic plane using boundary collocation method

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Abstract

The fracture behavior of a functionally graded magneto-elastic plane with multiple parallel cracks is examined in this article. Under anti-plane mechanical, in-plane electric, and magnetic loadings, it is assumed that the cracks are either of the magneto-electrically impermeable or permeable types. Here, three distinct crack configurations are taken into consideration. For each of the three crack configuration cases, the boundary collocation and least square methods are used to obtain the semi-analytical expressions of the stress intensity factors (SIFs) at the crack tips. SIFs are used to calculate the stress magnification factors (SMFs). The novelty of the article is the study of shielding and amplification tendencies of cracks under the impact of functionally graded parameter, geometric size, and electric and magnetic loads. The graphical illustrations of SMFs as a function of gradient parameter, the distance between the cracks, and electric and magnetic loadings for three different crack configurations are the key features of the article.

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Acknowledgements

The authors are extending their heartfelt thanks to the revered reviewers for their suggestions toward the improvement of the article. The second author (Subir Das) acknowledges the project grant provided by the National Board for Higher Mathematics (NBHM), Department of Atomic Energy, Government of India (File No. 02011/2/2022 NBHM (R.P.)/R &D II / 2171).

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  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Ritika Singh & Subir Das

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  1. Ritika Singh
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Correspondence to Ritika Singh.

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Singh, R., Das, S. Analysis of multiple parallel cracks in a functionally graded magneto-electro-elastic plane using boundary collocation method. Arch Appl Mech 93, 4497–4516 (2023). https://doi.org/10.1007/s00419-023-02506-0

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