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State-Space Approach to Generalized Thermoelasticity

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Encyclopedia of Thermal Stresses

Overview

The theory of coupled thermoelasticity was formulated by Biot [1] to eliminate the paradox inherent in the classical uncoupled theory that elastic changes have no effect on the temperature. Unfortunately, the heat equations for any of the two theories, though different, are of the diffusion type predicting infinite speeds of propagation for heat waves contrary to physical observations.

Two generalizations to the coupled theory were introduced. The first is due to Lord and Shulman [2] who obtained a wave-type heat equation by postulating a new law of heat conduction to replace the classical Fourier’s law. This new law contains the heat flux vector as well as its time derivative. It contains also a new constant that acts as a relaxation time. Since the heat equation of this theory is of the wave type, it automatically ensures finite speeds of propagation for heat and elastic waves. The remaining governing equations for this theory, namely, the equations of motion and the...

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Alexandria, Alexandria, Egypt

    Hany H. Sherief & A. M. Abd El-Latief

Authors
  1. Hany H. Sherief
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  2. A. M. Abd El-Latief
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Corresponding author

Correspondence to Hany H. Sherief .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY, USA

    Richard B. Hetnarski

  2. Naples, FL, USA

    Richard B. Hetnarski

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Sherief, H.H., Abd El-Latief, A.M. (2014). State-Space Approach to Generalized Thermoelasticity. In: Hetnarski, R.B. (eds) Encyclopedia of Thermal Stresses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2739-7_369

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