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Influence of boundary conditions on the solution of a hyperbolic thermoelasticity problem

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Abstract

We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord–Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically.

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Authors and Affiliations

  1. Department of Theoretical Mechanics, Peter the Great Saint-Petersburg Polytechnic University, Polytechnicheskaya, 29, St. Petersburg, Russia, 195251

    Evgeniy Yu. Vitokhin & Mikhail B. Babenkov

  2. Institute for Problems in Mechanical Engineering RAS, Bolshoy pr. V. O., 61, St. Petersburg, Russia, 199178

    Mikhail B. Babenkov

Authors
  1. Evgeniy Yu. Vitokhin
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  2. Mikhail B. Babenkov
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Correspondence to Evgeniy Yu. Vitokhin.

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Communicated by Andreas Öchsner.

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Vitokhin, E.Y., Babenkov, M.B. Influence of boundary conditions on the solution of a hyperbolic thermoelasticity problem. Continuum Mech. Thermodyn. 29, 457–475 (2017). https://doi.org/10.1007/s00161-016-0540-z

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  • DOI: https://doi.org/10.1007/s00161-016-0540-z

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