Title: Magneto-electro-elastic analysis for two mode-III semi-permeable collinear cracks in piezo-electro-magnetic strip

Authors: Pooja Raj Verma; Ravi Raj Verma

Addresses: Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, New Delhi-110017, India ' Department of Chemistry, Government P.G. College, Amethi, U.P., India

Abstract: A mode-III crack problem for piezo-electro-magnetic strip weakened by two transversely oriented semi-permeable collinear cracks under out-of-plane shear stress and in-plane electric-displacement and magnetic induction is addressed. The problem is formulated and then solved using Fourier series method and integral equation technique. Closed-form analytic expressions are derived for various fracture parameters viz. crack sliding displacement, crack opening potential drop, crack opening induction drop, field intensity factors and energy release rates. Numerical case study is presented graphically for BaTiO₃-CoFe₂O₄ piezo-electro-magnetic material to show the influence of inter-crack distance, volume fractions and electro-magnetic crack-face boundary conditions on crack sliding displacement, crack opening potential drop, crack opening induction drop and energy release rates. Moreover, the effect of prescribed mechanical loadings as well as electro-magnetic loadings on energy release rates are also presented graphically. Results obtained are presented graphically, analyzed and concluded.

Keywords: collinear cracks; Fourier series method; inter-crack distance; integral equation; piezo-electro-magnetic strip; semi-permeable crack; volume fraction.

DOI: 10.1504/IJMMNO.2020.106535

International Journal of Mathematical Modelling and Numerical Optimisation, 2020 Vol.10 No.2, pp.187 - 213

Received: 01 May 2019
Accepted: 25 Jul 2019
Published online: 09 Apr 2020 *

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