With the above quantities, it is possible to build a generalized Newtonian fluid model whose viscosity exhibits distinct behaviors in shear and extension. Here, one can, for example, combine the quantities given by equations Equation 32–3 and Equation 32–4 with appropriate algebra. A fluid model exhibiting a constant shear viscosity and strain hardening is found in   [10] and is given by:

(32–8)

where the quantity is the zero-shear viscosity, while the parameters and control the strain hardening. Its translation in CLIPS language for usage as a UDF involving the local stretch rate (as single dependence field) is typically given in the following example:

;
; Viscosity law referred to as 32.
;
; Follow the instructions; do not alter anything else
; (note that a real number MUST contain a "."; "2." differs from "2")
;
(deffunction viscosity (?e)
;
;          Specify here the zero-shear viscosity
    (bind ?eta0 1000.)
;
;          Specify here the strain hardening factor (positive)
    (bind ?m 2.)
;
;          Specify here the time constant for cosh function
    (bind ?lambda 3.)
    (bind ?R (* ?eta0 (cosh(* ?m ?lambda ?e)) ) )
?R
)

A fluid model exhibiting a shear thinning and strain hardening could be given by:

(32–9)

where and respectively denote the local shear rate and local stretch rate. The quantities , , , , and are the independent parameters of the law. The translation of Equation 32–9 in CLIPS language for usage as a UDF involving the local shear rate and local stretch rate is typically given by the following example:

;
; Viscosity law referred to as 31.
;
; Follow the instructions; do not alter anything else
; (note that a real number MUST contain a "."; "2." differs from "2")
;
(deffunction viscosity (?g ?e)
;
;          Specify here the zero-shear viscosity
    (bind ?eta0 1000.)
;
;          Specify here the viscosity at infinite shear
    (bind ?etainf 0.)
;
;          Specify here the strain hardening factor (positive)
    (bind ?m 0.4)
;
;          Specify here the time constant for Bird-Carreau
    (bind ?lambda 3.)
;
;          Specify here the power index for Bird-Carreau viscosity
    (bind ?n 0.7)
    (bind ?R (+ ?etainf (* (- ?eta0 ?etainf) (/ (* (** (+ 1. (**
    (* ?lambda ?g) 2.)) (/ (- ?n 1.) 2.) ) (cosh(* ?m ?lambda ?e)))
    (** (+ 1. (* 3. (** (* ?lambda ?e) 2.))) (/ (- ?n 1.) 2.))) )))
?R
)

When invoking the UDF function with two arguments (the local shear rate and local stretch rate) for such a law, it is important to select them in that sequence. It is also important to note that the last bind statement in the UDF file is actually written on one single line that terminates in this example with the six closing parentheses.

Eventually, a fluid model exhibiting a shear thinning and a constant elongation viscosity could be given by:

(32–10)

where and respectively denote the local shear rate and local stretch rate. The quantities , , , ? and are the independent parameters of the law. The translation of Equation 32–10 into CLIPS language for usage as a UDF involving the local shear rate and local stretch rate is typically given by the following example:

;
; Viscosity law referred to as 33.
;
; Follow the instructions; do not alter anything else
; (note that a real number MUST contain a "."; "2." differs from "2")
;
(deffunction viscosity (?g ?e)
;
;           Specify here the zero-shear viscosity
    (bind ?eta0 1000.)
;
;           Specify here the viscosity at infinite shear
    (bind ?etainf 0.)
;
;           Specify here the time constant for Bird-Carreau
    (bind ?lambda 3.)
;
;           Specify here the power index for Bird-Carreau viscosity
    (bind ?n .7)
    (bind ?R (+ ?etainf (* (- ?eta0 ?etainf) (** (/ (+ 1. (**
    (* ?lambda ?g) 2.)) (+ 1. (* 3. (** (* ?lambda ?e) 2.)) ) )
    (/ (- ?n 1.) 2.) ) )))
?R
)

When invoking the UDF function with two arguments (the local shear rate and local stretch rate) for such a law, it is important to select them in that sequence. It is also important to note that the last bind statement in the UDF file is actually written on one single line that terminates here with the five closing parentheses.

It is important to remember that these laws are analytically more complex than those involving the local shear rate only, and that this may have consequences on the numerical treatment.

Other laws can be created, but they are mainly a matter of algebra.