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E, G, K and μ elastic modulus, shear modulus, bulk modulus and Poisson’s ratio respectively. To express the stress strain relations completely for this material, at least __________

Correct Answer: Any two of the four must be known
As E = 2G(1 + μ) = 3K(1 – 2μ) = 9KG / (3K + G), if any two of these four are known, the other two can be calculated by the relations between them.

From an alloy, two specimens are machined and tested separately under tension and compression. The engineering stress-strain curves as well as the true stress-true strain curves for tension and compression are plotted in the same diagram. Identify the correct statements:
P. The engineering stress-strain curves in tension and compression are identical.
Q. The true stress-true strain curve in compression is lower than the true stresstrue strain curve in tension due to Bauschinger effect.
R. The true stress-true strain curve in tension is above the corresponding engineering stress-strain, curve.
S. The true stress-true strain curve in tension and compression are identical.

Three elastic constants for a completely anisotropic elastic material which follows the Hooke's law are young's modulus, elastic limit stress and yield stress. Which of the following properties is most sensitive to increase in strain rate ?

Which of the following relationships is correct for relating the three elastic constants of an isotropic elastic material (where, E = Young's modulus, G = Modulus of rigidity or shear modulus v = Poisson's ratio)?

Tresca or maximum-shear stress criteria assumes that yielding occurs when the maximum shear stress reaches a value of the shear stress in the uniaxial tension test. Assume the principal stress being σ1, σ2, σ3 where σ1 is largest, and σ3 is the smallest principal stresses. Find the value of minimum shear stress to cause yielding, given that yield stress in tension is equal to σo?

Elastic failure of a material occurs, when the tensile stress equals yield strength, yield point or the elastic limit. Also, the elastic failure occurs according to maximum strain theory, when the maximum tensile strain equals (where, $$\sigma $$ = yield strength and E = modulus of elasticity)

Poisson's ratio of a material is the ratio of unit lateral strain to the unit axial elongation within its elastic limit. The value of Poisson's ratio for structural and pressure vessel steel may be taken as

If E, N, K and $$\frac{1}{{\text{m}}}$$ are modulus of elasticity, modulus of rigidity. Bulk modulus and Poisson ratio of the material, the following relationship holds good

In a material of pure shear stress τthe strain energy stored per unit volume in the elastic, homogeneous isotropic material having elastic constants E and v will be:

The strain energy stored in a body due to shear stress, is (where $$\tau $$ = Shear stress, C = Shear modulus and V = Volume of the body)

A material has elastic constant of 100MPa and Poisson’s ratio as 10. Find the shear modulus of the material.