Micromechanics-based elastic model for functionally graded materials with particle interactions

Yin, Huiming; Sun, Lizhi; Paulino, Gláucio H.

doi:10.1016/j.actamat.2004.04.007

Cited by 109 publications

(73 citation statements)

References 25 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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“…Thus, focusing on this issue, some specific material models were developed to estimate the effective properties of FGMs. For instance, Yin et al [27] developed a material model based on the Eshelby's equivalent inclusion method with pairwise particle interaction, and Aboudi et al [26] developed a higherorder numerical cell theory. In this work, a rather simple and generic type of material model will be applied to estimate the effective properties of FGMs.…”

Section: A Functionally Graded Materials Modelmentioning

confidence: 99%

Optimization of material distribution in functionally graded structures with stress constraints

Stump

Silva

Paulino

2006

Commun. Numer. Meth. Engng.

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SUMMARYThis work describes a topology optimization framework to design the material distribution of functionally graded structures considering mechanical stress constraints. The problem of interest consists in minimizing the volumetric density of a material phase subjected to a global stress constraint. Due to the existence of microstructure, the micro-level stress is considered, which is computed by means of a mechanical concentration factor using a p-norm of the Von Mises stress criterium (applied to the micro-level stress). Because a 0-1 (void-solid) material distribution is not being sought, the singularity phenomenon of stress constraint does not occur as long as the material at any point of the medium does not vanish and it varies smoothly between material 1 and material 2. To design a smoothly graded material distribution, a material model based on a non-linear interpolation of the Hashin-Strikhman upper and lower bounds is considered. Consistently with the framework adopted here in, the so-called 'continuous approximation of material distribution' approach is employed, which considers a continuous distribution of the design variable inside the finite element. As examples, the designs of functionally graded disks subjected to centrifugal body force are presented. The method generates smooth material distributions, which are able to satisfy the stress constraint.

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“…Thus, some specific FGMs speciahzed material models have been developed such as Yin et al [13] and Aboudi et al [12].…”

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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Micromechanics-based elastic model for functionally graded materials with particle interactions

Cited by 109 publications

References 25 publications

Three-dimensional elastic solutions for functionally graded circular plates

Three-dimensional elastic solutions for functionally graded circular plates

Optimization of material distribution in functionally graded structures with stress constraints

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

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