Surface tension-induced interfacial stresses around a nanoscale inclusion of arbitrary shape

Abstract

Investigated in this paper is the surface tension-induced stress field around a nanoscale inclusion of arbitrary shape embedded in an infinite elastic plane, with an emphasis on the combined effects of surface tension and arbitrary inclusion shape. Muskhelishvili’s complex variable method is employed to formulate the basic equations that are solved with the aid of conformal mapping and series expansion methods. Accuracy of the present solution is verified by comparing its predictions with known results of an arbitrarily shaped hole. The surface tension-induced stress field is demonstrated for four shapes of inclusions (ellipse, approximately regular triangle, square and regular pentagon with round corners). The numerical results show that as the inclusion changes from a “soft” to a “hard” one (compared to the matrix), hoop and normal stresses along the inclusion–matrix interface on the inclusion side will increase, while those on the matrix side will decrease. However, shear stress along the inclusion–matrix interface does not considerably change as the inclusion changes from a “soft” to a “hard” one. It is also found that the maximum hoop stress on the matrix side of a “soft” inclusion and the maximum shear stress always occur nearby, but not exactly at the round corners where all other stresses for all four discussed inclusion shapes attain their maximums. Besides, for the four inclusion shapes discussed, shear stress along the inclusion–matrix interface vanishes at all corners as a consequence of the symmetry.