Development of three dimensional constitutive theories based on lower dimensional experimental data

TL;DR

This paper explores how various three-dimensional constitutive models, based on lower-dimensional experimental data, can be derived using entropy maximization principles, all reducing to Burgers' model in one dimension.

Contribution

It introduces different energy storage and dissipation choices within entropy maximization to generate multiple 3D constitutive models that unify under Burgers' model in 1D.

Findings

Multiple 3D models derived from entropy maximization.

All models reduce to Burgers' viscoelastic model in 1D.

Demonstrates the flexibility of entropy-based approaches in constitutive modeling.

Abstract

Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored energy and rate of entropy production, etc. In this paper we show different choices for the manner in which the body stores energy and dissipates energy and satisfies the requirement of maximization of the rate of entropy production that leads to many three dimensional models. All of these models, in one dimension, reduce to the model proposed by Burgers to describe the viscoelastic behavior of bodies.