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Eshelby’s inclusion problem in large deformations. (English) Zbl 1473.74024

Summary: In this contribution, we propose a multiplicative decomposition of the deformation gradient corresponding to the imagined procedure that J. D. Eshelby [Proc. R. Soc. Lond., Ser. A 241, 376–396 (1957; Zbl 0079.39606)] 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.

MSC:

74E05 Inhomogeneity in solid mechanics
74B20 Nonlinear elasticity
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74A05 Kinematics of deformation

Citations:

Zbl 0079.39606
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References:

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