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The effects of surface elasticity on the thermal stress around a circular nano-hole in a thermoelectric material

We analyze the contribution of surface elasticity and electric current density on the thermal stress distribution around a circular nano-hole in a thermoelectric material. Using complex variable methods, we obtain closed-form solutions describing the corresponding thermoelastic fields in the vicinity of the nano-hole. Our results indicate that the effect of surface elasticity is to generate significant normal and shear stresses on the boundary of the hole, allowing for the ability to either suppress or enhance hoop stress depending on the sign of the corresponding surface material constant. In addition, we find that positive hoop stress generated on the boundary by the remote electric current density can be neutralized by the incorporation of positive surface elasticity. In the case of the remaining boundary stress components, both surface elasticity and electric current density are found to enhance normal stress, while the maximum shear stress depends largely on the contribution of surface elasticity.