Stress Distribution between Gauss Quadrature Method and Alternate Method for Functionally Graded Material.

Human tibia, the second largest bone in human body, is made of complex biological material having inhomogeneity and anisotropy in such a manner that makes it a functionally graded material. While analyses of human tibia assuming it to be made of different material regions have been attempted in past, functionally graded nature of the bone in the mechanical analysis has not been considered. This study highlights the importance of functional grading of material properties in capturing the correct stress distribution from the finite element analysis (FEA) of human tibia under static loading. Isotropic and orthotropic material properties of different regions of human tibia have been graded functionally in three different manners and assigned to the tibia model. The nonfunctionally graded and functionally graded models of tibia have been compared with each other. It was observed that the model in which functional grading was not performed, uneven distribution and unrealistic spikes of stresses occurred at the interfaces of different material regions. On the contrary, the models with functional grading were free from this potential artifact. Hence, our analysis suggests that functional grading is essential for predicting the actual distribution of stresses in the entire bone, which is important for biomechanical analysis. We find that orthotropic nature of the bone tends to increase the maximum von Mises stress in the entire tibia, while inclusion of cross-sectional inhomogeneity typically increases the stresses across normal cross section. Accordingly, our analysis suggests that both orthotropy as well as cross-sectional inhomogeneity should be included to correctly capture the stress distribution in the bone.

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A functionally graded material model for the transmural stress distribution of the aortic valve leaflet

Journal of Biomechanics ◽

10.1016/j.jbiomech.2017.01.039 ◽

2017 ◽

Vol 54 ◽

pp. 88-95 ◽

Cited By ~ 25

Author(s):

Bruno V. Rego ◽

Michael S. Sacks

Keyword(s):

Aortic Valve ◽

Stress Distribution ◽

Functionally Graded Material ◽

Material Model ◽

Functionally Graded ◽

Valve Leaflet ◽

Aortic Valve Leaflet ◽

Graded Material

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Vibration analysis of an axially functionally graded material non-prismatic beam under axial thermal variation in humid environment

Journal of Vibration and Control ◽

10.1177/10775463211037150 ◽

2021 ◽

pp. 107754632110371

Author(s):

Rahul Singh ◽

Pankaj Sharma

Keyword(s):

Functionally Graded Material ◽

Temperature Rise ◽

Differential Quadrature Method ◽

Functionally Graded ◽

Quadrature Method ◽

Thermal Variation ◽

Harmonic Differential Quadrature Method ◽

Prismatic Beam ◽

Graded Material ◽

Axially Functionally Graded Material

The vibration analysis of an axially functionally graded material non-prismatic Timoshenko beam under axial thermal variation in humid environment is carried out using the harmonic differential quadrature method. In this modeling, the length and width of the beam remains constant whereas thickness of the beam is linearly varied along the axis of the beam. The material properties are temperature dependent and are assumed to be varied continuously along the axial direction according to power law distribution. Three types of temperature variations are considered in this study, that is, uniform temperature rise, linear temperature rise, and non-linear temperature rise. The temperature of the beam remains constant under uniform temperature rise condition and it is varied linearly and nonlinearly along the length of beam for rest of the conditions. The beam is subjected to uniform moisture concentration to impose humidity. Hamiltonian’s approach is used to derive the governing equations of motion. The resultant governing equations are then solved using the harmonic differential quadrature method to obtain the natural frequencies of the axially functionally graded material non-prismatic beam. The results obtained using the harmonic differential quadrature method are compared with results obtained for special cases. The effects of thermal variation, humidity, non-homogeneity parameter, and end conditions on natural frequencies of the non-prismatic beam are reported.

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Analysis of Temperature/Stress Distribution in a Stress-Relief-Type Functionally Graded Material Plate under Thermal Shock.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A ◽

10.1299/kikaia.65.2318 ◽

1999 ◽

Vol 65 (639) ◽

pp. 2318-2324 ◽

Cited By ~ 6

Author(s):

Hideo AWAJI ◽

Hiromitsu TAKENAKA ◽

Sawao HONDA ◽

Tadahiro NISHIKAWA

Keyword(s):

Stress Distribution ◽

Thermal Shock ◽

Temperature Stress ◽

Functionally Graded Material ◽

Stress Relief ◽

Functionally Graded ◽

Graded Material

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Elastoplastic Analysis of a Functionally Graded Material Beam Subjected to Uniformly Distributed Load

Journal of Mechanics ◽

10.1017/jmech.2019.40 ◽

2019 ◽

Vol 36 (1) ◽

pp. 73-85

Author(s):

L. J. Xue ◽

X. Y. Bian ◽

J. J. Feng ◽

J. N. Liu

Keyword(s):

Stress Distribution ◽

Functionally Graded Material ◽

Functionally Graded ◽

Average Stress ◽

Elastoplastic Material ◽

Elastoplastic Behavior ◽

Distributed Load ◽

Uniformly Distributed Load ◽

Graded Material ◽

Fgm Beam

ABSTRACTThe elastoplastic behavior of a Functionally Graded Material (FGM) simply supported beam consisting of elastic material A and elastoplastic material B under uniformly distributed load is investigated. A power function is used to describe the volume fractions of the constituent materials, and the average stress of the FGM beam is obtained by using the averaging method. This method can avoid the assumption of the varying properties of the whole material, and can consider the different Possion’s ratios of the different constituent materials. What’s more, only the elastoplastic material B in the FGM beam will yield, and the yield function is determined by the stress of material B only, rather than the average stress of the whole material. The method used in this work is more closer to the real material than the method by assuming the variation of the whole properties of FGM. The theoretical results show a good agreement with the finite element results, which indicates that the method provided in this work is valid. With this method, the variation of the elastic and plastic areas, the stress distribution on the cross section, variation of the curvature and neutral layer, and the residual stress distribution of the FGM beam are discussed through numerical results. This work can provide a new way for the design and in-depth investigation of FGM material.

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