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General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics

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Abstract

Based on the fundamental equations of piezoelasticity of quasicrystals (QCs), with the symmetry operations of point groups, the plane piezoelasticity theory of onedimensional (1D) QCs with all point groups is investigated systematically. The governing equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the operator method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form solutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.

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Author information

Authors and Affiliations

  1. School of Science, Inner Mongolia University of Technology, Hohhot, 010051, China

    Jing Yu, Junhong Guo & Yongming Xing

  2. College of General Education, Inner Mongolia Normal University, Hohhot, 010022, China

    Jing Yu

  3. Department of Civil Engineering, University of Akron, Akron, OH, 44325-3905, USA

    Ernian Pan

Authors
  1. Jing Yu
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  2. Junhong Guo
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  3. Ernian Pan
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  4. Yongming Xing
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Correspondence to Junhong Guo.

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Project supported by the National Nature Science Foundation of China (Nos. 11262012, 11262017, 11462020, and 10761005) and the Scientific Research Key Program of Inner Mongolia University of Technology (No. ZD201219)

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Yu, J., Guo, J., Pan, E. et al. General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics. Appl. Math. Mech.-Engl. Ed. 36, 793–814 (2015). https://doi.org/10.1007/s10483-015-1949-6

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  • DOI: https://doi.org/10.1007/s10483-015-1949-6

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