# A Symbolic Computation Framework for Constitutive Modelling Based On Entropy Principles

## TL;DR

This paper introduces a symbolic computational framework using Maple and GeM to automate the derivation of constitutive functions consistent with the entropy principle, simplifying complex symbolic calculations in material modeling.

## Contribution

It presents a novel software implementation of Liu's algorithm for symbolic computation, enabling automated derivation of entropy-compliant constitutive models.

## Key findings

- Automated derivation of explicit constitutive functions
- Simplification of Liu's identities through symbolic computation
- Application to physical examples demonstrating effectiveness

## Abstract

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.