Transversely isotropic elasticity tensors

1987 ◽  
Vol 411 (1840) ◽  
pp. 85-93 ◽  
Keyword(s):  
Isotropic Material ◽  
Transversely Isotropic ◽  
Representation Formula ◽  
Elasticity Tensor ◽  
Transversely Isotropic Material ◽  
Hyperelastic Materials ◽  
Isotropic Elasticity ◽  
Elasticity Tensors ◽  
Symmetry Transformations ◽  
Axis Of Symmetry

A representation formula for the elasticity tensor of a linearly elastic, transversely isotropic material is obtained, depending on eight constants. If, besides rotations about the axis of symmetry, reflections with respect to planes through that axis are also regarded as admissible symmetry transformations for the material, it is shown that the number of constants reduces to six. It is also shown that, no matter whether reflections belong to the collection of admitted symmetry transformations or not, only five constants are needed for hyperelastic materials.

Determination of Elastic Constants for Human Femurs

1979 ◽  
Vol 101 (3) ◽  
pp. 193-197 ◽  
Author(s):  
V. G. Lappi ◽  
M. S. King ◽  
I. Le May
Keyword(s):  
Elastic Properties ◽  
Elastic Constants ◽  
Isotropic Material ◽  
Rotational Symmetry ◽  
Transversely Isotropic ◽  
Longitudinal Axis ◽  
Transversely Isotropic Material ◽  
Axis Of Symmetry ◽  
Plane Of Isotropy

The elastic properties of the bone constituting human femurs have been determined from measurements of the velocities of ultrasonic compressional and shear waves through wet, embalmed bone samples. The bone has been shown to be a transversely isotropic material with the axis of symmetry parallel to the longitudinal axis of the bone. The values of the elastic constants were determined to be: c11=6860±330MPaE3=5500MPac12=2700±570MPaE1=4990MPac13=3760±1570MPaν31=0.39c33=8480±760MPaν12=0.20c44=2240±180MPaG31=2240MPa where the 3-axis is that of rotational symmetry and the 1- and 2-axes are in the plane of isotropy.

THE ANALYSIS OF DYNAMICAL RESPONSE OF TRANSVERSELY ISOTROPIC MATERIAL UNDER BLASTING LOAD

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1443-1448
Author(s):  
YUE-XIU WU ◽  
QUAN-SHENG LIU
Keyword(s):  
Isotropic Material ◽  
Peak Velocity ◽  
Transversely Isotropic ◽  
Normal Direction ◽  
Dynamical Response ◽  
Transversely Isotropic Material ◽  
Peak Acceleration ◽  
Loading Direction ◽  
Blasting Load ◽  
Explosion Load

To understand the dynamic response of transversely isotropic material under explosion load, the analysis is done with the help of ABAQUS software and the constitutive equations of transversely isotropic material with different angle of isotropic section. The result is given: when the angle of isotropic section is settled, the velocity and acceleration of measure points decrease with the increasing distance from the explosion borehole. The velocity and acceleration in the loading direction are larger than those in the normal direction of the loading direction and their attenuation are much faster. When the angle of isotropic section is variable, the evolution curves of peak velocity and peak acceleration in the loading direction with the increasing angles are notching parabolic curves. They get their minimum values when the angle is equal to 45 degree. But the evolution curves of peak velocity and peak acceleration in the normal direction of the loading direction with the increasing angles are overhead parabolic curves. They get their maximum values when the angle is equal to 45 degree.

scholarly journals Elastic-plastic transition stresses in a transversely isotropic thick-walled cylinder subjected to internal pressure and steady-state temperature

2009 ◽  
Vol 13 (4) ◽  
pp. 107-118 ◽  
Author(s):  
Thakur Pankaj
Keyword(s):  
Steady State ◽  
Internal Pressure ◽  
Isotropic Material ◽  
Internal Surface ◽  
Transversely Isotropic ◽  
Percentage Increase ◽  
Transversely Isotropic Material ◽  
Elastic Plastic ◽  
Steady State Temperature ◽  
Walled Cylinder

Elastic-plastic transitional stresses in a transversely isotropic thick-walled cylinder subjected to internal pressure and steady-state temperature have been derived by using Seth's transition theory. The combined effects of pressure and temperature has been presented graphically and discussed. It has been observed that at room temperature, thick-walled cylinder made of isotropic material yields at a high pressure at the internal surface as compared to cylinder made of transversely isotropic material. With the introduction of thermal effects isotropic/transversely isotropic cylinder yields at a lower pressure whereas cylinder made of isotropic material requires less percentage increase in pressure to become fully-plastic from its initial yielding as compared to cylinder made of transversely isotropic material.

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