Open AccessPolygonal inclusions with nonuniform eigenstrains in an isotropic half plane
Author(s) -
Yonggang Lee,
Bin Xu,
Wenming Zou
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1634/1/012152
Subject(s) - isotropy , cartesian coordinate system , plane (geometry) , mathematical analysis , mathematics , superposition principle , inclusion (mineral) , geometry , boundary value problem , displacement (psychology) , boundary (topology) , physics , optics , psychology , psychotherapist , thermodynamics
Polygonal inclusion problem in an isotropic half plane is investigated in this paper. The eigenstrains prescribed in the inclusion are assumed to be characterized by polynomials of arbitrary order in the Cartesian coordinate system. Based on a novel superposition method, the solution of the inclusion problem in a half plane is decomposed into two subproblems: the inclusion problem in a full plane and the auxiliary boundary problem in the half plane. Furthermore, the Kolosov-Muskhelishvili (K-M) potentials for the full plane and the auxiliary potentials for the half plane along with their derivatives are expressed into two sets of basic functions, which involve the boundary integrals of the inclusion domain. For polygonal inclusions, exact explicit expressions for both basic functions are explicitly derived, which leads to those for the induced displacement, strain and stress fields.