Micromechanical models for graded composite materials

Reiter, Thomas; Dvorak, George J.; Tvergaard, Viggo

doi:10.1016/s0022-5096(97)00007-0

Cited by 218 publications

(85 citation statements)

References 22 publications

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“…), it is possible to describe the behaviour of each macroscopic material point by means of its relevant effective properties obtained via standard homogenisation techniques for statistically homogeneous aggregates. Instead, care must be taken in estimating the effective properties within regions where the microstructure varies rapidly (see, e.g., Reiter et al 1997;Yin et al 2004).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional elastic solutions for functionally graded circular plates

Sburlati¹,

Bardella²

2011

European Journal of Mechanics - A/Solids

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Three-dimensional elastic solutions are obtained for a functionally graded thick circular plate subject to axisymmetric conditions. We consider a isotropic material where the Young modulus depends exponentially on the position along the thickness, while the Poisson ratio is constant. The solution method utilises a Plevako's representation form which reduces the problem to the construction of a potential function satisfying a linear fourth-order partial differential equation. We write this potential function in terms of Bessel functions and we pointwise assign mixed boundary conditions. The analytic solution is obtained in a general form and explicitly presented by assuming transversal load on the upper face and zero displacements on the mantle; this is done by superposing the solutions of problems with suitably imposed radial displacement. We validate the solution by means of a finite element approach; in this way, we highlight the effects of the material inhomogeneity and the limits of the employed numerical method near the mantle, where the solution shows a large sensitivity to the boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional elastic solutions for functionally graded circular plates

Sburlati¹,

Bardella²

2011

European Journal of Mechanics - A/Solids

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“…In addition, those conventional models, such as Mori-Tanaka and selfconsistent, have been apphed to estimate the effective FGM properties in several works [6,7,8,9,10]. However, these models were originally developed for statistically homogeneous materials and are not able to capture the material gradient nature of the FGMs [Il].…”

Section: A Functionally Graded Materlvl Modelmentioning

confidence: 99%

“…Considering the macro-stress ((o)) given by (0) = C^-*^(£), where (E) is the macrostrain obtained from the analysis of the equivalent structure made of homogenous material with constitutive relations C^-*^. From the relation of C^-*^, C^, and C" the matrices B^ and B" can be derived such that [7],…”

Section: A Functionally Graded Materlvl Modelmentioning

confidence: 99%

Topology Optimization with Stress Constraints: Reduction of Stress Concentration in Functionally Graded Structures

Stump

Silva

Paulino³

2008

AIP Conference Proceedings

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Abstract. This presentation describes a topology optimization framework to design the material distribution of functionally graded structures with a tailored Von Mises stress field. The problem of interest consists in obtaining smooth continuous material fraction distribution that produces an admissible stress field. This work explores the topology optimization method for minimizing volume fraction of one of the phases considering stress constraints. Existence of inherent material microstructure requires consideration of the micro level stress field, which is computed through a mechanical concentration factor based on the local stress in each phase of the material. Thus, p-norm of the Von Mises stress in the microstructure is considered as a global constraint. To illustrate the method and discuss its essential features, we present engineering examples of axisymmetric FGM structures subjected to body forces.

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“…Here an RVE in a continuum body is a material volume that statistically represents the neighbourhood of a material point. The microstructure can be periodic [21][22][23], random [24,25] or even functionally graded materials [12,26,27]. From the relation between averaged stress and strain, we can derive an effective mechanical constitutive law of the RVE [28].…”

Section: Introductionmentioning

confidence: 99%

Boundary effect on the elastic field of a semi-infinite solid containing inhomogeneities

2015

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The boundary effect of one inhomogeneity embedded in a semi-infinite solid at different depths has firstly been investigated using the fundamental solution for Mindlin's problem. Expanding the eigenstrain in a polynomial form and using the Eshelby's equivalent inclusion method, one can calculate the eigenstrain and thus obtain the elastic field. When the inhomogeneity is far from the boundary, the solution recovers Eshelby's solution. The method has been extended to a many-particle system in a semi-infinite solid, which is first demonstrated by the cases of two spheres. The comparison of the asymptotic form solution with the finite-element results shows the accuracy and capability of this method. The solution has been used to illustrate the boundary effects on its effective material behaviour of a semi-infinite simple cubic lattice particulate composite. The local field of a semi-infinite composite has been calculated at different volume fractions. A representative unit cell has been taken with different depths to the surface. The average stress and strain of the unit cell have been calculated under uniform loading conditions of normal or shear force on the surface, respectively. The effective elastic moduli of the unit cell not only depend on the material proportion, but also on its distance to the surface. The present model can be extended to other types of particle distribution and ellipsoidal particles.

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Micromechanical models for graded composite materials

Cited by 218 publications

References 22 publications

Three-dimensional elastic solutions for functionally graded circular plates

Three-dimensional elastic solutions for functionally graded circular plates

Topology Optimization with Stress Constraints: Reduction of Stress Concentration in Functionally Graded Structures

Boundary effect on the elastic field of a semi-infinite solid containing inhomogeneities

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