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A spherical elastic
inhomogeneity with interface slip and diffusion under a
deviatoric far-field load
Xu Wang and Peter Schiavone |
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Vol. 19 (2024), No. 3, 531–540
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Abstract |
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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. |
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Keywords
spherical elastic inhomogeneity, interface slip and
diffusion, deviatoric far-field load, relaxation time,
state-space equation, uniform stress state
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Milestones
Received: 24 January 2024
Revised: 4 March 2024
Accepted: 8 March 2024
Published: 27 March 2024
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Authors |
| Xu Wang | |
| School of Mechanical and Power
Engineering East China University of Science and Technology Shanghai, 200237 China |
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| Peter Schiavone | |
| Department of Mechanical
Engineering University of Alberta 10-203 Donadeo Innovation Center for Engineering Edmonton, AB T6G 1H9 Canada |
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| © 2024 MSP (Mathematical Sciences Publishers). |
