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Modified Green–Lindsay analysis of an electro-magneto elastic functionally graded medium with temperature dependency of materials

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This article presents a modified Green–Lindsay (MG-L) thermoelasticity model considering temperature and strain rate. Previously, this model has been developed based on the Green–Lindsay theory of thermoelasticity using strain and temperature rate dependent thermoelastic equations. This study analyzes stress and thermal wave propagation of a functionally graded medium exposed to an electromagnetic field and a thermal shock. All magnetic, elastic, and thermal features of the medium are considered to vary in the longitudinal direction. Additionally, the properties of the material are dependent on the temperature in the form of a cubic function. Using the large displacement formulation and the finite strain theory (FST), nonlinear coupled equations are obtained. Considering FST, strain rate, temperature rate, and temperature dependence of materials leads to a highly nonlinear system of coupled magneto-thermoelastic equations. These equations are solved by employing a combination of the updated finite element method, finite difference, as well as Picard’s iterations. The obtained results show considerable impacts of the strain rate, temperature rate, and temperature dependence of materials on the responses of the nonlinear system. Graphically, the numerical results are presented for displacement, stress, and temperature components under the impact of a magnetic field. Based on the results, the impact of magnetic fields on the responses of FG elastic material heated by a thermal shock is evident. In addition, the stress and the thermal wave speed grow by increasing the volume fraction in the FG structures.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Yazd University of Iran, Yazd, Iran

    Mina Mirparizi

  2. Department of Mechanical Engineering, Sharif University of technology, Tehran, Iran

    Seyed Mehdi Razavinasab

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  1. Mina Mirparizi
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  2. Seyed Mehdi Razavinasab
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Correspondence to Mina Mirparizi.

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Mirparizi, M., Razavinasab, S.M. Modified Green–Lindsay analysis of an electro-magneto elastic functionally graded medium with temperature dependency of materials. Mech Time-Depend Mater 26, 871–890 (2022). https://doi.org/10.1007/s11043-021-09517-w

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