Eshelby's inclusion problem in large deformations

In this contribution, we propose a multiplicative decomposition of the deformation gradient corresponding to the imagined procedure that Eshelby (Proc R Soc Ser A 241:376-396, 1957) used to investigate the theory of inclusions in the case of infinitesimal deformations. The proposed multiplicative decomposition is inspired by classical multiplicative decompositions reported in the literature and encompasses, as particular cases, other decompositions proposed for Eshelby's inclusion problem. The linearisation of the proposed multiplicative decomposition coincides with the additive decomposition of the infinitesimal strain in Eshelby's original procedure.

Automated summary

In this contribution, a multiplicative decomposition of the deformation gradient is proposed, inspired by Eshelby's investigation on inclusions. This decomposition includes other proposed decompositions for Eshelby's inclusion problem as special cases, with its linearization coinciding with Eshelby's original additive decomposition of infinitesimal strain.