Consider a cube of isotropic material with only Normal Stress and component acti
ID: 1843234 • Letter: C
Question
Consider a cube of isotropic material with only Normal Stress and component acting on it. Take the following as the State of Stress: where are known real numbers. Take the isotropic material elastic constants to be E and v.
(a.) Define the Hydrostatic Stress and the Volumetric Strain.
(b.) Express the State of Stress in terms of the Deviatoric Stress and the Hydrostatic Stress.
(c.) Are there values of A and B such that the cube of material will never experience a Deviatoric stress at any orientation? If so, what is the condition to determine the values of A and B? For this A and B, what does the stress state become? For this A and B, what does the Volumetric Strain expression become?
Explanation / Answer
(a.) Hydrostatic Stress: It is the average of three normal stress components also being compressive in nature so it becomes negative pressure.Because the hydrostatic stress is isotropic, it acts equally in all directions. Hydrostatic stress causes a change in volume of a material, which if expressed per unit of original volume gives a volumetric strain denoted by Ev
Volumetric Strain: Volumetric strain of a deformed body is defined as the ratio of the change in volume of the body to the deformation to its original volume. If V is the original volum and dV the change in volume occurred due to the deformation, the volumetric strain ev induced is given by ev =dV/V
(b.) Hydrostatic Stress: It is the average of three normal stress components also being compressive in nature so it becomes negative pressure.Because the hydrostatic stress is isotropic, it acts equally in all directions.
hyd=(11+22+33)/3
Deviatoric Stress: Deviatoric stress is what's left after subtracting out the hydrostatic stress. The deviatoric stress will be represented by .
=hyd
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