Question

What is the strain formula?

Answer 1

Hint: The strain is the ratio of change in the parameter (length, angle, volume) by the original content (length, angle, volume). There are three types of strain and each strain deals with the different types of parameters.

Complete answer:
The general definition of strain is: the length of stretch by the original length. The mathematical representation of the same is,
$$\epsilon ={\displaystyle \frac{\delta }{L}}$$
Where $$\delta$$ is the length of the stretch and L is the original length.
Strains are always unitless. There are three types of strain. They are linear, shear and volume.
In the case of linear strain, the symbol used to represent the strain is epsilon. The change in length by the original length is called the linear strain. The mathematical representation of the same is,
$$\epsilon ={\displaystyle \frac{\mathrm{\Delta }l}{l_0}}$$
In the case of shear strain, the symbol used to represent the strain is gamma. The change in angle by the original angle (originally perpendicular) is called the shear strain. The mathematical representation of the same is,
$$\gamma ={\displaystyle \frac{\mathrm{\Delta }x}{y}}$$.
In the case of volume strain, the symbol used to represent the strain is theta. The change in volume by the original volume is called the volume strain. The mathematical representation of the same is,
$$\theta ={\displaystyle \frac{\mathrm{\Delta }V}{V_0}}$$.
$$\therefore$$The strain formula is $$\epsilon ={\displaystyle \frac{\delta }{L}}$$, with $$\delta$$being the length of the stretch and L being the original length.

Additional information:
Basically there are 3 types of stress associated with the three types of moduli. They are: Young’s modulus, Shear modulus and the Bulk modulus. In the case of Young’s modulus, stress is normal to the opposite faces and the strain is the length. In the case of shear modulus, the stress is tangential to the opposite faces and strain is tangent. Similarly, in the case of bulk modulus, the stress is normal to all faces and the strain is volume.

Note:
In most of the cases, the types of particular will be similar, whereas, in the case of strain, it has opposite types of linear strain. Those types are: extension and contraction. The extension means to get longer. The contraction means to get shorter.