A Symbolic Computation Framework for Constitutive Modelling Based On Entropy Principles

The entropy principle in the formulation of M\"{u}ller and Liu is a common tool used in constitutive modelling for the development of restrictions on the unknown constitutive functions describing material properties of various physical continua. In the current work, a symbolic software implementation of the Liu algorithm, based on \verb|Maple| software and the \verb|GeM| package, is presented. The computational framework is used to algorithmically perform technically demanding symbolic computations related to the entropy principle, to simplify and reduce Liu's identities, and ultimately to derive explicit formulas describing classes of constitutive functions that do not violate the entropy principle. Detailed physical examples are presented and discussed.