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Fracture Mechanics at Atomic Scales

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From Creep Damage Mechanics to Homogenization Methods

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 64))

Abstract

Fracture and strength in atomic components are governed by mechanical instabilities at atomic scales associated with irreversible deformations through bond breaking/switching, such as cleavage, dislocation nucleation, and phase transformations of crystal lattices. It is therefore of central importance to determine the critical conditions where atomic structures becomes mechanically unstable. Here we review the state-of-the-art theory for “fracture mechanics of atomic structures” that provides a rigorous description of mechanical instabilities in arbitrary atomic structures under any external loading/constraint. The theory gives the critical instability condition by positivity of the minimum eigenvalue of the Hessian matrix of the total energy with respect to degrees of freedom of the system (i.e., instability criterion), and it successfully provides atomistic insights into fracture in various atomic/nanoscale structures. The review also covers the recent development of theory extended to advanced systems including large-scale, finite temperature, and “multi-physics” instabilities in (ferro-)electric and magnetic materials as functional fracture.

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Acknowledgments

The authors acknowledge financial support of this work by the Grant-in-Aid for Specially Promoted Research (Grant No. 25000012) from the Japan Society of Promotion of Science (JSPS).

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Authors and Affiliations

  1. Department of Mechanical Engineering and Science, Kyoto University, Nishikyo-ku, Kyoto, 615-8540, Japan

    Takahiro Shimada & Takayuki Kitamura

Authors
  1. Takahiro Shimada
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  2. Takayuki Kitamura
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Correspondence to Takahiro Shimada .

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Editors and Affiliations

  1. Otto-von-Guericke-Universität Magdeburg, Fakultät für Maschinenbau, Institut für Mechanik, Lehrstuhl für Technische Mechanik, Universitätsplatz 2, 39106 Magdeburg, Germany

    Holm Altenbach

  2. Department of Engineering Mechanics and Energy, University of Tsukuba, Tsukuba, Japan

    Tetsuya Matsuda

  3. Department of Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

    Dai Okumura

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Shimada, T., Kitamura, T. (2015). Fracture Mechanics at Atomic Scales. In: Altenbach, H., Matsuda, T., Okumura, D. (eds) From Creep Damage Mechanics to Homogenization Methods. Advanced Structured Materials, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-319-19440-0_17

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  • DOI: https://doi.org/10.1007/978-3-319-19440-0_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19439-4

  • Online ISBN: 978-3-319-19440-0

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