Skip to main content
Article
General Solutions of Plane Problem in One-Dimensional Quasicrystal Piezoelectric Materials and Its Application on Fracture Mechanics
Applied Mathematics and Mechanics
  • Jing Yu
  • Junhong Guo
  • Ernian Pan, University of Akron Main Campus
  • Yongming Xing
Document Type
Article
Publication Date
6-1-2015
Disciplines
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.
Citation Information
Jing Yu, Junhong Guo, Ernian Pan and Yongming Xing. "General Solutions of Plane Problem in One-Dimensional Quasicrystal Piezoelectric Materials and Its Application on Fracture Mechanics" Applied Mathematics and Mechanics Vol. 36 Iss. 6 (2015) p. 793 - 814
Available at: http://works.bepress.com/ernian_pan/9/