Development of three dimensional constitutive theories based on lower dimensional experimental data
For researchers in continuum mechanics, this work reveals a fundamental ambiguity in inferring 3D constitutive laws from 1D/2D experiments, though the result is incremental as it extends existing entropy-based frameworks.
The paper shows that different choices for stored energy and dissipation, under maximization of entropy production, lead to many 3D constitutive models that all reduce to Burgers' 1D viscoelastic model, highlighting the non-uniqueness of 3D models derived from lower-dimensional data.
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.