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Applied Mathematics and Mechanics >

2019 , Vol. 40 >Issue 8: 1097 - 1118

DOI: https://doi.org/10.1007/s10483-019-2507-6

Articles

Modified strip saturated models for two equal collinear cracks with coalesced zones in piezoelectric media

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  • 1. Department of Sciences and Humanities, National Institute of Technology Uttarakhand, Srinagar 246174, India;
    2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India

Received date: 2018-11-26

  Revised date: 2019-03-03

  Online published: 2019-08-01

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Abstract

Two equal collinear cracks with coalesced interior electric saturation zones are analytically studied for two-dimensional (2D) arbitrary polarized semipermeable piezoelectric media based on a modified strip saturated model. The strip saturated model is modified here by varying the strip saturated constant electric displacement condition to the polynomially varying electric displacement conditions. Based on the linear, quadratic, and cubic electric displacement conditions on the inner and outer saturated zones, different modified strip saturated models are proposed and studied for two equal collinear cracks. With the Stroh formalism and the complex variable technique, these fracture problems are reduced into different types of non-homogeneous Riemann Hilbert problems in unknown generalized complex potential functions. These mathematical problems are then solved with the Riemann-Hilbert approach to obtain the stress and electric displacement components at any point of the domain. The explicit expressions for the outer saturated zone length, the crack opening potential (COP), the crack opening displacement (COD), and the local intensity factors (LIFs) are derived. A numerical study is presented for the modified strip saturated model in 2D arbitrary polarized semipermeable PZT-4 material. The obtained results are compared with those of the strip saturated model, and the effects of the polynomially varying saturation condition on the saturated zones and the applied electrical loadings are presented.

Key words： analytical mechanics; nonholonomic system; integral; inverse problem; complex variable; piezoelectric; strip saturated model; coalesced zone; Riemann-Hilbert problem

Cite this article

S. SINGH, K. SHARMA, R. R. BHARGAVA . Modified strip saturated models for two equal collinear cracks with coalesced zones in piezoelectric media[J]. Applied Mathematics and Mechanics, 2019 , 40(8) : 1097 -1118 . DOI: 10.1007/s10483-019-2507-6

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