On eshelby's in a three-phase cylindrically concentric solid, and the elastic moduli of fiber-reinforced composites

Luo, Huiwu; Weng, George J.

doi:10.1016/0167-6636(89)90008-2

Cited by 88 publications

(34 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The coefficients of the potential functions are identified by the imposed boundary conditions. The analytical solutions are shown to be able to reproduce the results obtained by Luo and Weng [16] as well as Markenscoff and Dundurs [20] if the exterior matrix is set to be unbounded. In addition, firm agreements are achieved with FEM results for concentric 2D finite domains.…”

Section: Introductionsupporting

confidence: 50%

“…When the deviatoric eigenstrains are considered in the inclusion or the interfacial zone, and the boundary conditions are prescribed as ε (0) i j = 0 at infinity, it is difficult to conduct the direct comparison because tedious calculation is needed to find out the inverse matrices in the theoretical solutions given by Luo and Weng [16] and Markenscoff and Dundurs [19]. Alternatively, the displacements at three arbitrarily selected points are compared when the material properties of the constituent phases are specified.…”

Section: Theoretical Formulation Of a 3-phase Concentric Rvementioning

confidence: 99%

“…If the volume fractions of the inhomogeneity and interfacial zone in the composite solids are not negligible, the solutions for unbounded 3-phase RVEs obtained by Luo and Weng [15,16] and by Markenscoff and Dundurs [20] cannot be directly applied. Recently, based on a series of investigations on 2D [25,26] and 3D [27,28] bounded RVEs, Li et al [28] proposed a shell model to study the average behavior of bounded n-phase concentric composite RVEs, which is indeed an approximate application of EIM.…”

Section: Introductionmentioning

confidence: 97%

“…For an unbounded matrix, if the embedded inhomogeneity and its surrounding interfacial zone form a concentric configuration, Luo and Weng [15,16] gave the analytical solutions for an arbitrary uniform eigenstrain within the inclusion for both 2D and 3D domains. In their investigation, the stress function-based formulation proposed by Christenson and Lo [17] is employed, and the eigenstrain within the inclusion is decomposed into dilatational and deviatoric components.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Disturbed elastic fields in a circular 2D finite domain containing a circular inhomogeneity and a finite interfacial zone

Pan

2014

Acta Mech

View full text Add to dashboard Cite

In order to take into account the effect of a finite interfacial zone between the inhomogeneity and matrix in an inhomogeneous representative volume element (RVE), analytical solutions for a 3-phase inclusion problem are needed. In this study, the primary focus is placed on a 3-phase concentric configuration for a 2D RVE, for which the exterior matrix is bounded and different elastic properties are assigned to the interior inclusion, interfacial zone and exterior matrix. In addition to the inhomogeneity induced by material mismatch, arbitrary uniform eigenstrains are allowed to occur independently within the interfacial zone and inclusion, respectively. In this study, the analytical solution is pursued via the complex potential method with the aid of 2 auxiliary potential functions. Based on the Sokhotski-Plemelj theorem, the complex potentials in each phase are constructed to account for the eigenstrains existing in the inclusion and the interfacial zone, as well as the imposed boundary conditions on the exterior matrix. The identification of the coefficients in the complex potential functions gives the analytical expressions for the disturbance induced by the inhomogeneity and eigenstrains. When compared with FEM simulations, a firm agreement is achieved for 3-phase concentric 2D finite domains. Furthermore, if the exterior matrix is extended to infinity, the obtained analytical solution reproduces the results given by Luo and Weng for uniform eigenstrain within the inclusion and by Markenscoff and Dundurs for uniform eigenstrain in the interfacial zone.

show abstract

Section: Introductionsupporting

confidence: 50%

Section: Theoretical Formulation Of a 3-phase Concentric Rvementioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Disturbed elastic fields in a circular 2D finite domain containing a circular inhomogeneity and a finite interfacial zone

Pan

2014

Acta Mech

View full text Add to dashboard Cite

show abstract

“…The Eshelby tensor for a fiber-reinforced material with an isotropic homogenous matrix, S 3 , was obtained by Luo and Weng [1989]. Alternative micromechanical methods that could be applied to the analysis of a fiber-reinforced material with the isotropic particulate matrix properties determined as shown above include the well-known Halpin-Tsai or mechanics of materials solutions.…”

Section: Micromechanics Of a Fiber-reinforced Particulate-matrix Matmentioning

confidence: 99%

Effect of elastic or shape memory alloy particles on the properties of fiber-reinforced composites

Birman¹

2009

J. Mech. Solids Struct.

View full text Add to dashboard Cite

The paper presents a comprehensive formulation for the analysis of the stiffness and strength of fiberreinforced composites with the matrix enhanced by adding elastic or shape memory alloy (SMA) spheroidal particles. The micromechanical model used to evaluate the stiffness tensor of the matrix with embedded particles is based on the Benveniste version of the Mori-Tanaka theory. In the case of a superelastic shape memory alloy particulate matrix, the stiffness of the particles depends on the martensitic fraction that is in turn affected by the state of stress within the particle. In this case an exact solution for the stiffness tensor of the composite material with elastic fibers and matrix and embedded SMA particles is developed combining the recent macromechanical solution for multi-phase composites with the inverse method of the analysis of SMA. In the particular case, this solution results in explicit formulae for the homogeneous material constants of a SMA particulate material subjected to axial loading. Upon the completion of the stiffness analysis the strengths of a fiber-reinforced material with the matrix containing elastic or SMA particles can be analyzed using the Eshelby solution for the stresses. As follows from numerical examples, elastic spherical particles added to the matrix of a fiber-reinforced composite significantly improve the transverse strength and stiffness of the material, even if the volume fraction of such particles is relatively small. The effect of elastic particles on the longitudinal strength and stiffness is less pronounced. It is also illustrated that the stress-induced transformation of superelastic SMA particles results in significant changes of the properties of SMA particulate composites.

show abstract

N‐Phase decagonal quasicrystalline circular inclusions under thermomechanical loadings

Wang

Schiavone

2012

Z Angew Math Mech

View full text Add to dashboard Cite

In this work a simple and effective method is proposed to solve the problem corresponding to plane strain deformations of an N‐phase decagonal quasicrystalline circular inclusion‐matrix system in which the circular inclusion is bonded to the surrounding matrix through (N‐2) co‐axial interphase layers. We consider three kinds of thermomechanical loadings: (i) the matrix is subjected to a remote uniform stress field; (ii) the composite undergoes a uniform temperature change; (iii) the matrix is subjected to a uniform heat flux at infinity. We find that it is sufficient to manipulate three 8 × 8 real matrices, a 5 × 5 real matrix, and another 4 × 4 real matrix to arrive at the complete temperature and thermoelastic fields within the circular inclusion and the surrounding matrix, irrespective of the number of interphase layers existing within the composite system. Our results clearly indicate that the existence of the intermediate interphase layer(s) mean that the internal stresses within the circular inclusion are: (i) sextic functions of the two coordinates x1 and x2 under the loading of a remote uniform stress field; (ii) quadratic functions of the two coordinates under the loading of a uniform temperature change; (iii) cubic functions of the two coordinates under the loading of a remote uniform heat flux. The design of neutral and harmonic coated circular inclusions is also discussed as an application of the derived solution. Our analysis suggests that a coated inclusion can be made neutral only to a remote isotropic phonon stress field; whereas it can be made harmonic to any remote uniform phonon stress field.

show abstract

On eshelby's in a three-phase cylindrically concentric solid, and the elastic moduli of fiber-reinforced composites

Cited by 88 publications

References 19 publications

Disturbed elastic fields in a circular 2D finite domain containing a circular inhomogeneity and a finite interfacial zone

Disturbed elastic fields in a circular 2D finite domain containing a circular inhomogeneity and a finite interfacial zone

Effect of elastic or shape memory alloy particles on the properties of fiber-reinforced composites

N‐Phase decagonal quasicrystalline circular inclusions under thermomechanical loadings

Contact Info

Product

Resources

About