Stress-driven diffusion in a deforming and evolving elastic circular tube of single component solid with vacancies |
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Authors: | Chien H Wu |
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Affiliation: | (1) Department of Civil and Materials Engineering (MC 246), University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607-7023, USA |
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Abstract: | The title problem is considered for an elastic circular tube of inner radius A and outer radius B. The tube is made of a single component solid with vacancies as its second component. The mole fraction of the massive species
is denoted by x
1, while that of the vacancies by x
0 = 1 – x
1. The tube is completely surrounded by vacuum, serving as a reservoir of vacancies. One of the standard elasticity boundary
conditions is applied at time t = 0, when the composition is uniform. The ensuing coupled deformation and diffusion leads to the evolving of A(t), B(t) and x
1(R, t) as functions of time. Since the single component solid is not in contact with its vapor or liquid, the diffusion boundary
condition is always tied to the elasticity problem through a surface condition that involves the normal configurational traction.
Our chemical potential has an energy density term that serves as a source in the interior and the boundary conditions for
the diffusion problem are such that the time rates of boundary accretion Ȧ(t) and Ḃ(t) must simultaneously satisfy two dissipative inequalities, one governed by the gradient of the internal chemical potential
and the other by the normal configurational traction. |
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Keywords: | Energy momentum tensor Configurational stress Chemical potential Diffusion |
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