A stochastic micromechanical model for elastic properties of functionally graded materials

2007 ◽  
Vol 39 (6) ◽  
pp. 548-563 ◽  
Author(s):  
S. Rahman ◽  
A. Chakraborty
Keyword(s):  
Elastic Properties ◽  
Functionally Graded Materials ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Graded Materials

Investigation of Stress Behavior in the Vicinity of Singular Points of Elastic Bodies Made of Functionally Graded Materials

2018 ◽  
Vol 85 (6) ◽  
Author(s):  
Andrey Yu. Fedorov ◽  
Valerii P. Matveenko
Keyword(s):  
Elastic Properties ◽  
Functionally Graded Materials ◽  
Dissimilar Materials ◽  
Functionally Graded ◽  
Singular Points ◽  
Polar Coordinates ◽  
Graded Materials ◽  
Numerical Investigations ◽  
Elastic Bodies ◽  
Stress Behavior

This paper presents the results of analytical and numerical investigations into stress behavior in the vicinity of different types of singular points on two-dimensional (2D) elastic bodies made of functionally graded materials (FGMs). A variant of constructing eigensolutions for plane FGM wedges, where the elastic properties are represented as a series expansion with respect to the radial coordinates, was considered. It was shown that, in the vicinity of singular points, the stress behavior is determined by solving the problem for the corresponding homogeneous wedge, where the elastic characteristics coincide with the characteristics of FGMs at the wedge vertex. Numerical investigations were carried out to evaluate the stress state of elastic bodies containing FGM elements at singular points, where the type of boundary conditions changes or where dissimilar materials come into contact. The results of the calculations showed that the behavior of stresses in FGMs in the vicinity of singular points can also be determined from an analysis of the eigensolutions for the corresponding homogeneous wedges, where the elastic properties coincide with the elastic constants of FGMs at singular points and that the functionally graded properties are dependent on one or two polar coordinates.

scholarly journals A micropolar model for elastic properties in functionally graded materials

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401878952 ◽  
Author(s):  
Shengyao Fan ◽  
Zhanqi Cheng
Keyword(s):  
Particle Size ◽  
Elastic Properties ◽  
Functionally Graded Materials ◽  
Effective Properties ◽  
Matrix Material ◽  
Functionally Graded ◽  
Two Phase ◽  
Graded Materials ◽  
Micromechanics Model ◽  
Matrix Zone

By considering the description of phase volume fractions, a micromechanics model is presented for predicting the elastic mechanical properties of isotropic two-phase functionally graded materials. The particle size dependence of the overall elasticity of functionally graded materials is not generally considered by classical continuum micromechanics; however, being based on micropolar theory, the presented micromechanics model is able to study such size effects. As the effective material properties vary gradually along the gradation direction, a functionally graded material can be divided into two distinct zones: the particle–matrix zone and the transition zone. In the particle–matrix zone, the matrix material is idealized as a micropolar continuum and Mori–Tanaka’s method is extended to the micropolar medium to evaluate the effective elastic properties. The effective properties across the gradation forms are further derived and the effects of particle size on the effective properties of a functionally graded materials are also studied. The validity and effectiveness of the present model is demonstrated by comparing the model results with other model outputs and experimental data.

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