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A spherical elastic inhomogeneity with interface slip and diffusion under a deviatoric far-field load

Xu Wang and Peter Schiavone

Vol. 19 (2024), No. 3, 531–540
Abstract

We study the problem of a spherical elastic inhomogeneity with simultaneous interface slip and diffusion embedded in an infinite elastic matrix subjected to a uniform deviatoric far-field load. The inhomogeneity and the matrix have separate elastic properties. Using the representations for displacements and tractions given by Christensen and Lo (1979), the original boundary value problem is ultimately reduced to a state-space equation which is then solved analytically. The field variables in the inhomogeneity and the matrix decay with two relaxation times. As time approaches infinity, the stresses inside the spherical inhomogeneity are completely relaxed to zero. Our solution recovers existing solutions in the literature when the inhomogeneity is rigid or when the inhomogeneity and the matrix have the same elastic properties. The internal spatially uniform and time-decaying stress field inside the spherical inhomogeneity is achieved when the radius of the spherical inhomogeneity is appropriately designed corresponding to interface diffusion and drag parameters.

Keywords
spherical elastic inhomogeneity, interface slip and diffusion, deviatoric far-field load, relaxation time, state-space equation, uniform stress state
Milestones
Received: 24 January 2024
Revised: 4 March 2024
Accepted: 8 March 2024
Published: 27 March 2024
Authors
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
Shanghai, 200237
China
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
10-203 Donadeo Innovation Center for Engineering
Edmonton, AB T6G 1H9
Canada