Eshelby problem in continuous shape transition of helical inclusion

Change in Eshelby tensor associated with continuous shape transition from cylinder to helix was numerically computed by means of Green's function method, where helical shape transition is demonstrated by horizontal and vertical shape transitions parameters, delta=(1-d/D) and rho=(1-d/p), respectively (d: helical core diameter, D: helical diameter, p: helical pitch). Regardless of the number of helical turns, significant change in Eshelby tensor was observed under the continuous shape transition from straight cylinder to mild twisted helix. In the meanwhile, the Eshelby tensor associated with the shape transition from the hollow-tube cylinder to the strong twisted helix is greatly influenced by the number of helical turns. By assuming spatial distribution of eigenstrain for the helix embedded in the cylinder, average internal stress inside and outside of helix was predicted by means of Tanaka-Mori theorem. (C) 2020 Elsevier Ltd. All rights reserved.