TY - JOUR
T1 - A chemo-mechanics framework for elastic solids with surface stress
AU - Gao, Xiang
AU - Fang, Daining
AU - Qu, Jianmin
N1 - Publisher Copyright:
© 2015 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2015/10/8
Y1 - 2015/10/8
N2 - Elasticity problems involving solid-state diffusion and chemo-mechanical coupling have wide applications in energy conversion and storage devices such as fuel cells and batteries. Such problems are usually difficult to solve because of their strongly nonlinear characteristics. This study first derives the governing equations for three-dimensional chemo-elasticity problems accounting for surface stresses in terms of the Helmholtz potentials of the displacement field. Then, by assuming weak coupling between the chemical and mechanical fields, a perturbation method is used and the nonlinear governing equations are reduced to a system of linear differential equations. It is observed from these equations that the mechanical equilibrium equations of the first two orders are not dependent on the chemical fields. Finally, the above chemo-mechanics framework is applied to study the stress concentration problem of a circular nano-hole in an infinitely large thick plate with prescribed mechanical and chemical loads at infinity. Explicit expressions up to the third order are obtained for the stress and solute concentration fields. It is seen from these solutions that, different from the classical elasticity result, the stress concentration factor near the nano-hole depends on the surface stress, applied tensile load and prescribed solute concentration at infinity.
AB - Elasticity problems involving solid-state diffusion and chemo-mechanical coupling have wide applications in energy conversion and storage devices such as fuel cells and batteries. Such problems are usually difficult to solve because of their strongly nonlinear characteristics. This study first derives the governing equations for three-dimensional chemo-elasticity problems accounting for surface stresses in terms of the Helmholtz potentials of the displacement field. Then, by assuming weak coupling between the chemical and mechanical fields, a perturbation method is used and the nonlinear governing equations are reduced to a system of linear differential equations. It is observed from these equations that the mechanical equilibrium equations of the first two orders are not dependent on the chemical fields. Finally, the above chemo-mechanics framework is applied to study the stress concentration problem of a circular nano-hole in an infinitely large thick plate with prescribed mechanical and chemical loads at infinity. Explicit expressions up to the third order are obtained for the stress and solute concentration fields. It is seen from these solutions that, different from the classical elasticity result, the stress concentration factor near the nano-hole depends on the surface stress, applied tensile load and prescribed solute concentration at infinity.
KW - Asymptotic analysis
KW - Chemical potential
KW - Chemo-mechanics
KW - Stress concentration
KW - Surface effect
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U2 - 10.1098/rspa.2015.0366
DO - 10.1098/rspa.2015.0366
M3 - Article
AN - SCOPUS:84946055833
SN - 1364-5021
VL - 471
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2182
M1 - 20150366
ER -