NDLI: Exact solution of Eshelby–Christensen problem in gradient elasticity for composites with spherical inclusions

Content Provider	Springer Nature Link
Author	Lurie, Sergey Volkov Bogorodskii, Dmitrii Tuchkova, Natalia
Copyright Year	2015
Abstract	The gradient elasticity theory is employed to solve exactly the problem of Eshelby–Christensen for filled composites with spherical inclusions across length scales. Relying on the fundamental symmetry considerations and using Lagrange’s variational formalism, we derive the governing relations of linear isotropic gradient elasticity. We demonstrate that to avoid spurious solutions, one should necessarily impose some additional symmetry restrictions on the operational strain gradient elastic constants that can be considered as a new correctness condition. By enforcing the “strain gradient” symmetry condition, we offer the variant of the correct applied one-parametric gradient theory of interfacial layer model. To solve the Eshelby–Christensen problem, we employ the generalized Eshelby’s integral representations for the gradient elasticity models that allow to formulate the closing equations in a self-consistent three-phase method, and we also use the generalized Papkovich–Neuber representation to determine the general form of the gradient solution and the structure of the scale effects. As a result, we obtained for the first time an exact solution of Eshelby–Christensen problem for composites reinforced with spherical inclusions in framework of the gradient interfacial layer model. There are known analogs of fundamental results for gradient models related to closed solution for composites with spherical inclusions obtained by R.M. Christensen and K.H. Lo in 1976. The obtained analytical solution of Eshelby–Christensen problem for correct gradient theory is used to determine the stress–strain state and the effective properties of dispersed composites. The analysis of the effect of scale factors is given; the error associated with the use of gradient theories that do not obey the proposed condition of correctness is estimated.
Starting Page	127
Ending Page	138
Page Count	12
File Format	PDF
ISSN	00015970
Journal	Acta Mechanica
Volume Number	227
Issue Number	1
e-ISSN	16196937
Language	English
Publisher	Springer Vienna
Publisher Date	2015-08-07
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical and Applied Mechanics Classical Continuum Physics Continuum Mechanics and Mechanics of Materials Structural Mechanics Vibration, Dynamical Systems, Control Engineering Thermodynamics, Heat and Mass Transfer
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Computational Mechanics

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