Write the relation between bulk modulus or youngs modulus
Answers
Virtually all common materials, such as the blue rubber band on the right, become narrower in cross section when they are stretched. The reason why, in the continuum view, is that most materials resist a change in volume as determined by the bulk modulus K (also called B) more than they resist a change in shape, as determined by the shear modulus G.
stretch honeycomb effect of Poisson's ratioIn the structural view, the reason for the usual positive Poisson's ratio is that inter-atomic bonds realign with deformation. Stretching of yellow honeycomb by vertical forces, shown on the right, illustrates the concept. Negative Poisson's ratio in designed materials and in some anisotropic materials is by now well known.
Poisson's ratio: relation to elastic moduli in isotropic solids
Poisson's ratio is related to elastic moduli K (also called B), the bulk modulus; G as the shear modulus; and E, Young's modulus, by the following (for isotropic solids, those for which properties are independent of direction). The elastic moduli are measures of stiffness. They are ratios of stress to strain. Stress is force per unit area, with the direction of both the force and the area specified. See Sokolnikoff Ref. [1]; also further details.
n = (3K - 2G)/(6K + 2G)
E = 2G( 1 + n)
E = 3K(1 - 2 n)
Further interrelations among elastic constants for isotropic solids are as follows. B is the bulk modulus.
elasticity interrelations with Poisson's ratio 1 elasticity interrelations with Poisson's ratio 2 elasticity interrelations with Poisson's ratio 3
The theory of isotropic linear elasticity allows Poisson's ratios in the range from -1 to 1/2 for an object with free surfaces with no constraint. Physically the reason is that for the material to be stable, the stiffnesses must be positive; the bulk and shear stiffnesses are interrelated by formulae which incorporate Poisson's ratio. Objects constrained at the surface can have a Poisson's ratio outside
Answer:
Young's modulus ( E ) describes tensile elasticity, or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. ... The bulk modulus is an extension of Young's modulus to three dimensions.