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.

在这个贡献中，我们提出了变形梯度的乘法分解，对应于 Eshelby (Proc R Soc Ser A 241:376–396, 1957) 用来研究无限小变形情况下的夹杂物理论的想象过程。提议的乘法分解受到文献中报道的经典乘法分解的启发，并且在特定情况下包括为 Eshelby 包含问题提出的其他分解。所提出的乘法分解的线性化与 Eshelby 原始程序中无穷小应变的加法分解相吻合。