Question: Simultaneous plot of parametric equations

The attached worksheet uses several procedures to develop a solution which is presented as a parametric plot of two procedures ("alpha" and "strain").  The current solution uses some constants declared at the beginning of the file which I would like to vary and then generate multiple plots associated with the different constants. 

As an example, I have attached a figure of such a plot from a journal article;  in this case, the relationship of the buckle angle (alpha) and the strain (epsilon) is plotted for rings of varying radii.

Is there a way to execute the plot() command and generate plots of several "versions" of your functions, varying only in the constants that are used?

Thank you for your assistance.

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