Analyzing the frequency band gap in functionally graded materials with harmonically varying material properties

2017 ◽  
Author(s):  
M.h. Ansari ◽  
M. Amin Karami
Keyword(s):  
Band Gap ◽  
Functionally Graded Materials ◽  
Frequency Band ◽  
Material Properties ◽  
Functionally Graded ◽  
Graded Materials

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

Thermoelastic Fracture Mechanics for Nonhomogeneous Material Subjected to Unsteady Thermal Load

1999 ◽  
Vol 67 (1) ◽  
pp. 87-95 ◽  
Author(s):  
B. L. Wang ◽  
J. C. Han ◽  
S. Y. Du
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Crack Problem ◽  
Laminated Composite ◽  
Functionally Graded ◽  
Comprehensive Treatment ◽  
Numerical Illustration ◽  
Graded Materials ◽  
Nonhomogeneous Material ◽  
Crack Problems

This article provides a comprehensive treatment of cracks in nonhomogeneous structural materials such as functionally graded materials. It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using a laminated composite plate model to simulate the material nonhomogeneity, we present an algorithm for solving the system based on the Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problems in the functionally graded materials with arbitrarily varying material properties. The algorithm can be applied to steady state or transient thermoelastic fracture problem with the inertial terms taken into account. As a numerical illustration, transient thermal stress intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of nonhomogeneous material with properties varying in the thickness direction. [S0021-8936(00)01601-9]

Numerical Investigation on the Fracture Behaviors of Three-Dimensional Functionally Graded Materials

2007 ◽  
Vol 353-358 ◽  
pp. 1098-1101 ◽  
Author(s):  
Hong Jun Yu ◽  
Li Cheng Guo ◽  
Lin Zhi Wu
Keyword(s):  
Functionally Graded Materials ◽  
Crack Front ◽  
Material Properties ◽  
High Efficiency ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Parameter Analysis ◽  
Graded Materials ◽  
Gaussian Integration ◽  
Fracture Behaviors

Functionally graded materials (FGMs) with continuous varying properties have absorbed great attention for the purpose of eliminating the mismatch of material properties which may result in cracking. In this paper, three-dimensional finite element method (3D FEM) based on nonhomogeneous elements is used to study the fracture behaviors of a 3D FGM plate. Since real material properties at Gaussian integration points are adopted during forming the element stiffness matrix, the nonhomogeneous material properties can be applied in each element. Moreover, 20-node singular elements are used around the crack front to deal with the singularity of stress fields at the crack front. By this way, the stress intensity factors (SIFs) can be calculated with high efficiency and accuracy. Therefore, compared with the general FEM using homogeneouos elements, the calculating efficiency and accuracy can be increased. Finally, parameter analysis is conducted. It is found that the material nonhomogeneity constant and the crack parameter have significant influences on the SIFs.

A Simplified Method for Calculating the Crack-Tip Field of Functionally Graded Materials Using the Domain Integral

1999 ◽  
Vol 66 (1) ◽  
pp. 101-108 ◽  
Author(s):  
P. Gu ◽  
M. Dao ◽  
R. J. Asaro
Keyword(s):  
Finite Element ◽  
Functionally Graded Materials ◽  
Material Properties ◽  
Crack Tip ◽  
Functionally Graded ◽  
Crack Tip Field ◽  
Graded Materials ◽  
Fine Mesh ◽  
Domain Integral ◽  
Standard Domain

A finite element based method is proposed for calculating stress intensity factors of functionally graded materials (FGMs). We show that the standard domain integral is sufficiently accurate when applied to FGMs; the nonhomogeneous term in the domain integral for nonhomogeneous materials is very small compared to the first term (the standard domain integral). In order to obtain it, the domain integral is evaluated around the crack tip using sufficiently fine mesh. We have estimated the error in neglecting the second term in terms of the radius of the domain for the domain integration, the material properties and their gradients. The advantage of the proposed method is that, besides its accuracy, it does not require the input of material gradients, derivatives of material properties; and existing finite element codes can be used for FGMs without much additional work. The numerical examples show that it is accurate and efficient. Also, a discussion on the fracture of the FGM interlayer structure is given.

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