The principle of equivalent eigenstrain for inhomogeneous inclusion problems

Ma, Lifeng; Korsunsky, Alexander M.

doi:10.1016/j.ijsolstr.2014.08.023

Cited by 41 publications

(28 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The substrate zone ρ N ρ 2 is eigenstrain-free. By the equivalent eigenstrain principle (Ma and Korsunsky [19]), the inhomogeneous inclusion problem in Fig. 5(a) can be transformed into the corresponding homogeneous inclusion problem as shown in Fig.…”

Section: The Inhomogeneous Inclusion Problem With Complex Eigenstrainmentioning

confidence: 99%

“…For simplicity, we just present the transform equation and ignore the manipulation details as (the details can be found in the reference: Ma and Korsunsky [19])…”

Section: The Inhomogeneous Inclusion Problem With Complex Eigenstrainmentioning

confidence: 99%

“…Recently the current authors published the equivalent eigenstrain principle, which allows transforming the inhomogeneous inclusion problem into a homogeneous inclusion problem (Ma and Korsunsky [19]). The idea of the transform is to replace the inhomogeneous inclusion with a homogeneous one which has a new equivalent eigenstrain distribution that can be solved using Green's function method (Mura [10]; Ru [20]; Li and Anderson [21]; Kuvshinov [22]; Ma [23]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Plane deformation of circular inhomogeneous inclusion problems with non-uniform symmetrical dilatational eigenstrain

Wang

Korsunsky

2015

Materials & Design

Self Cite

View full text Add to dashboard Cite

Section: The Inhomogeneous Inclusion Problem With Complex Eigenstrainmentioning

confidence: 99%

“…For simplicity, we just present the transform equation and ignore the manipulation details as (the details can be found in the reference: Ma and Korsunsky [19])…”

Section: The Inhomogeneous Inclusion Problem With Complex Eigenstrainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Plane deformation of circular inhomogeneous inclusion problems with non-uniform symmetrical dilatational eigenstrain

Wang

Korsunsky

2015

Materials & Design

Self Cite

View full text Add to dashboard Cite

“…The strain field inside an ellipsoidal inhomogeneity subject to an external load can be obtained by transforming the problem into the corresponding equivalent inclusion problem 7,8 .…”

Section: Introductionmentioning

confidence: 99%

Applicability of the interface spring model for micromechanical analyses with interfacial imperfections to predict the modified exterior Eshelby tensor and effective modulus

Lee¹,

Kim

Lee

et al. 2019

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

Closed-form solutions for the modified exterior Eshelby tensor, strain concentration tensor, and effective moduli of particle-reinforced composites are presented when the interfacial damage is modeled as a linear spring layer of vanishing thickness; the solutions are validated against finite element analyses. Based on the closed-form solutions, the applicability of the interface spring model is tested by calculating those quantities using finite element analysis (FEA) augmented with a matrix-inhomogeneity non-overlapping condition. The results indicate that the interface spring model reasonably captures the characteristics of the stress distribution and effective moduli of composites, despite its well-known problem of unphysical overlapping between the matrix and inhomogeneity. external strain, , to the average internal strain field inside the inhomogeneity, , as , : , where , is the interior strain concentration tensor and is given in terms of the interior Eshelby tensor, , , and elastic stiffness tensors, and , of the matrix and the inhomogeneity, respectively 8 . Hence, given the importance of the Eshelby tensor, a primary focus of recent research has been the derivation of the simplified form of , for various material properties and geometries of the inclusion 9-11 .The strain field of the matrix around the inclusion has also been studied because the strain field outside of the inclusion plays a critical role in determining the mechanical properties beyond the elastic response regime. It is also important for considering composites with high reinforcement volume fractions, in which the interaction among the reinforcements becomes important. The non-uniform strain field at a position in the matrix can be expressed with a similar form as , : * , where the superscript "Ext" refers to the exterior, and , is the exterior Eshelby tensor 12, 13 . The exterior Eshelby tensor and the exterior strain concentration tensor, , , have been used to consider the shear localization of metallic glass, the matrix failure point for reinforced composites, and the interaction among the reinforcements [14][15][16] .Further progress on the inclusion or inhomogeneity problem has been achieved by considering the interfacial damage present in realistic composites where debonding or slip between the matrix and inclusion can occur. As a simplified model of interfacial imperfection, J. Qu introduced a linear-spring layer of vanishing thickness at the interface to represent the displacement jump between the inclusion and the matrix 17, 18 . Zero and infinite interfacial spring compliance correspond to perfect and completely damaged (i.e., no load transfer between the matrix and the inclusion) interfaces, respectively. Owing to its mathematical simplicity and easier physical interpretation (compared to the interface stress model 19,20 and the interphase model 21,22 ), the interface spring model has been widely adopted to describe composites with an imperfect interface 17,18,[23][24][25][26] . In earlier studies, the modified interior Eshelb...

show abstract

“…It has been applied to a variety of situations, in particular in the context of joining and welding [16][17][18]. In parallel with this applied research, fundamental aspects of direct and inverse eigenstrain theory have been elucidated [19,20]. It has become apparent that eigenstrain provides a broad basis for simulating the relationship between inelastic strains (eigenstrains) induced in the structure by diffusion, transformation, or thermal mismatch, and the concomitant ''live'' or residual stresses.…”

Section: Discussionmentioning

confidence: 99%

Explicit formulae for the internal stress in spherical particles of active material within lithium ion battery cathodes during charging and discharging

2015

Self Cite

View full text Add to dashboard Cite

The principle of equivalent eigenstrain for inhomogeneous inclusion problems

Cited by 41 publications

References 28 publications

Plane deformation of circular inhomogeneous inclusion problems with non-uniform symmetrical dilatational eigenstrain

Plane deformation of circular inhomogeneous inclusion problems with non-uniform symmetrical dilatational eigenstrain

Applicability of the interface spring model for micromechanical analyses with interfacial imperfections to predict the modified exterior Eshelby tensor and effective modulus

Explicit formulae for the internal stress in spherical particles of active material within lithium ion battery cathodes during charging and discharging

Contact Info

Product

Resources

About