Mechanical Properties of Matter

Elasticity and plasticity: 

The property of a body, by virtue of  which  it tends to regain its original size and shape when the applied force is removed, is known as elasticity.Plasticity is the tendency of a material deform permanently under the application of external load.For example, a solid piece of metal being bent into a new shape displays plasticity as permanent changes occur within the material itself. 

Stress and Strain:

When a  body  is  subjected  to  a  deforming  force,  a restoring force equal  in  magnitude but opposite in direction to the applied forces developed in the body. This restoring force per unit area is known as stress.

If  F is the force applied and A  is the  area of cross section of  the body,

                                                     Magnitude of the stress = F/A

Strain describes relative deformation or change in shape and size of  materials under applied forces.

Hooke’s law:

Hooke’s law states that, for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load. Under these conditions the object returns to its original shape and size upon removal of the load.

Mathematically, Hooke’s law " F = kx " where  F = applied force  x=change in length

                                            Or "F= - kx "  where F=Restoring force equal opposite of applied

Hooke’s law may also be expressed in terms of stress and strain."For relatively small stresses, stress is proportional to strain"

stress = k × strain     where k is the proportionality constant and is known as modulus of elasticity.

Young's modulus: 

 It is defined as the ratio of the stress (force per unit area) along an axis over the strain (ratio of deformation over initial length) along that axis in the range of stress in which Hooke's law holds.

The slope of the stress–strain curve at any point is called the tangent modulus. The tangent modulus of the initial(O to A), linear portion of a stress–strain curve is called Young's modulus.

Y is the Young's modulus (modulus of elasticity)

F is the force exerted on an object under tension;

A0 is the original cross-sectional area through which the force is applied;

ΔL is the amount by which the length of the object changes;

L0 is the original length of the object.

Similar to Young Modulus sheer modulus for shearing stress and bulk modulus for hydraulic stress

Shear Modulus Or  modulus of rigidity(G):

Bulk Modulus (B):

  

The negative sign indicates the fact that withan increase in pressure, a decrease in volume
occurs.

Poisson's Ratio(v): Poisson's ratio, is the negative ratio of transverse to axial strain.

Relation between Young's modulus,sheer modulus,bulk modulus