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

Where ‘E’ is Young’s modulus of elasticity.

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 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 enormous when compared to elastic strain values.