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A double coated circular elastic inhomogeneity with internal uniform deviatoric stresses

Xu Wang and Peter Schiavone

Vol. 18 (2023), No. 5, 741–749
Abstract

We show that the internal deviatoric stresses within a double coated circular elastic inhomogeneity can remain uniform when the infinite elastic matrix is subjected to a uniform remote deviatoric load. The internal uniform stress field remains valid when the relative thickness of the outer coating is determined through the solution of a cubic equation for given material parameters and the relative thickness of the inner coating. The explicit expression for the internal uniform deviatoric stress field within the circular inhomogeneity is presented and demonstrated graphically. We also accomplish the design of a harmonic double coated circular inhomogeneity with internal uniform stresses. In this second design, both the relative thickness of the outer coating and the ratio of the shear modulus of the matrix to that of the outer coating are determined by solving two coupled nonlinear equations numerically.

Keywords
double coated circular inhomogeneity, deviatoric load, uniform stress field, harmonic inhomogeneity, complex variable method
Milestones
Received: 9 June 2023
Revised: 8 August 2023
Accepted: 13 August 2023
Published: 25 October 2023
Authors
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
Shanghai
China
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
Edmonton, AB
Canada