On Constitutive Equations and Dimensional Analysis

A method of obtaining a system of partial differential equations from the invariance of a constitutive function under some restrictions of a continuous group of transformations is shown. Using the theory of partial differential equations, a set of independent solutions and dependence relationship is derived. Group theory technique is employed relative to dimensional analysis to show how the transformation from one unit system to another results in a relationship among different dimensional variables. An alternative proof of Buckingham's Pi-theorem is presented.