Hooke’s law is the proportionality gives the relationship between elastic strain (ε) and stress (σ):

where ‘E’ is Young’s modulus of elasticity of the material.

The following power-law equation, known as ** Holloman-Ludwig equation**, describes the material behavior in the plastic range:

^{n}

Where ‘K’ is the strength coefficient, and n is the strain hardening exponent which can have values from n = 0 (perfectly plastic solid) to n = 1 (elastic solid). For most metals, n has values between 0.10 and 0.50.

A variation from the above power-law equation is also known as **Ludwig equation**

_{y}+ K.ε

^{n}

Where ‘σ_{y}‘ is the yield strength of the material. The true strain ε used in the above equation should actually be the plastic strain value, given by the following equation,

_{p}= ε – ε

_{e}≈ ε

where elastic strains (ε_{e}) can be safely neglected because plastic strains are very large when compared to elastic strain values.