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Applied Mathematics and Mechanics

, Volume 36, Issue 6, pp 793–814 | Cite as

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

  • Jing Yu
  • Junhong GuoEmail author
  • Ernian Pan
  • Yongming Xing
Article

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.

Key words

quasicrystals (QCs) piezoelasticity fracture mechanics crack complex variable method 

Chinese Library Classification

O346.1 

2010 Mathematics Subject Classification

74A45 74A40 74S70 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Jing Yu
    • 1
    • 2
  • Junhong Guo
    • 1
    Email author
  • Ernian Pan
    • 3
  • Yongming Xing
    • 1
  1. 1.School of ScienceInner Mongolia University of TechnologyHohhotChina
  2. 2.College of General EducationInner Mongolia Normal UniversityHohhotChina
  3. 3.Department of Civil EngineeringUniversity of AkronAkronUSA

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