The starting point to derive an expression for the equivalent plastic strain is the plastic work equivalence

(3–73)

In the case of uniaxial tensile loading (using a material coordinate system as in Figure 3.3: Injection molded specimens needed for the uniaxial tension experiments).

(3–74)

so that the left hand side of Equation 3–73 simplifies to . Similarly, the equivalent stress Equation 3–61 simplifies to

(3–75)

On the other hand, using the flow rule, Equation 3–58, with , we can relate the plastic strain increment to the plastic multiplier

(3–76)

Inserting Equation 3–76 into the plastic work equivalence, Equation 3–73, it follows that . Moreover, in case of uniaxial tensile loading, the first component of the flow rule, Equation 3–76, yields the following relation:

(3–77)

In summary, for a uniaxial tensile load, the equivalent stress and equivalent accumulated plastic strain read:

(3–78)

where and are the experimental stress and plastic strain. See [Ottosen 2005, chapter 12] for further details.