A constitutive equation is needed for the degree of transformation x. The following equation is suggested in [12]:

(11–13)

where	= dimensionless model parameter (usually equal to 0.06)
	= a time constant
	G = melt shear modulus
	m = a constant (usually equal to 1)

This transport equation is strongly coupled with both amorphous and semicrystalline phases through the trace of .

The degree of transformation x is governed by a highly nonlinear advection equation. To reduce the level of nonlinearity in Equation 11–13, select a unit value for m. At rest (quiescent condition), this equation indicates that x evolves towards , which is seen as the upper limit of crystallization. To facilitate the convergence of the solver, you can apply an evolution scheme on the parameter .

The time constant is the inverse of the Avrami constant under quiescent conditions and depends on the temperature in nonisothermal flows. In [12], the temperature dependence of the Avrami constant is described using a Gaussian function.

You can interpret the Avrami constant as an indication of the maximum crystallization rate. Consequently, an inverse Gaussian function is used for the temperature dependence of :

(11–14)

where is the temperature that corresponds to the peak in the Gaussian function, is its width around . The factor takes the value of -1.

A large value of time constant means that the information is transported without any change. To prevent the sudden use of a large time constant in the calculation, an evolution scheme can be defined on . The degree of transformation can change only when the temperature is close to .