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Wave Dynamics of Deformation and Fracture

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Dynamical Processes in Generalized Continua and Structures

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 103))

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Abstract

Deformation and fracture of solids are formulated comprehensively as wave dynamics based on a gauge field theoretical approach. With the application of the least action principle, a set of field equations are derived, which describe the dynamics of deformation that propagates as a wave. The elasticity and plasticity are characterized by the form of the longitudinal force term of the field equations. For elasticity, the longitudinal term represents elastic force proportional to the volume expansion. For plasticity, the longitudinal force term represents the velocity damping force that causes the irreversibility of plastic deformation and the decaying feature in the wave characteristics. The oscillatory feature of plasticity comes from the elastic shear force. The fracture is characterized as the final stage of plastic deformation where the solid totally loses the restoring mechanism. Consequently, the dynamics loses the oscillatory feature and the displacement becomes unidirectional generating material discontinuity. A number of supporting experimental observations are presented.

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Notes

  1. 1.

    See Ref. [9] for more detailed explanation about \(D_0\).

  2. 2.

    The arrows are drawn longer here to emphasize that the displacement is greater on the left side. The lengths are not to scale as compared with above region “1”.

  3. 3.

    The fringes in the \(\textit{u}\) pattern also indicate counterclockwise rotation.

  4. 4.

    The aluminum alloy 7705 (Al-Zn-Mg-Cu alloy) specimen was first solid-solution treated and hardened by nano-scale precipitates up to the peak hardness (7075 T6). Subsequently, the alloy was over-aged at 400 \(^\circ \)C for 30 min to soften the matrix by coarsening the precipitates (7075 T7).

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Acknowledgements

The present theoretical development has been made with the help of a number of people. The author owes a debt of gratitude to all of them. In particular, the author is extremely grateful to Academician V. E. Panin for the introduction of his original theory that the present theory stemmed out, and Professor V. E. Egorushkin for his guidance that helped the author to deepen his understanding of the gauge field theory. The author also highly appreciate Professor C. A. Sciammarella for his continuous encouragement and fruitful discussions. It is unfortunate that the space is not enough to mention more people that I would like to express my gratitude.

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Authors and Affiliations

  1. Department of Chemistry and Physics, Southeastern Louisiana University, SLU 10878, Hammond, LA, 70402, USA

    Sanichiro Yoshida

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  1. Sanichiro Yoshida
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Correspondence to Sanichiro Yoshida .

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Editors and Affiliations

  1. Lehrstuhl Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    Alexander Belyaev

  3. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Victor A. Eremeyev

  4. Department of Theoretical Mechanics, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Anton Krivtsov

  5. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    Alexey V. Porubov

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Yoshida, S. (2019). Wave Dynamics of Deformation and Fracture. In: Altenbach, H., Belyaev, A., Eremeyev, V., Krivtsov, A., Porubov, A. (eds) Dynamical Processes in Generalized Continua and Structures. Advanced Structured Materials, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-030-11665-1_28

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  • DOI: https://doi.org/10.1007/978-3-030-11665-1_28

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