On the History of Material Theory – A Critical Review

Material theory in a strict sense is not older than just half a century and from the beginning characterized by fundamental disputes and changes of paradigms. A number of different suggestions have been made and - often - forgotten soon after their publication. In this article the main existing theories shall be briefly described and critically discussed. Some important demands for an adequate theory are raised and applied to these suggestions.

Originally, two totally different lines of approaches existed, namely that of

history functionals

and that of

inner variables

or

state theories

. Since both approaches suffer from fundamental deficiencies, neither of them really achieved global acceptance. And for a long time it remained unclear how the two approaches could be mutually related.

This was changed in 1972 by Noll’s

New Theory of Simple Materials

[19], in which a third approach was suggested that made it possible to compare the two preceding formats. The gain in generality was, however, accompanied by a loss of simplicity. Consequently, this theory has been used only by very few groups within the scientific community.

Since then the majority of the papers in the field of material modeling are pragmatic and do not claim for general validity. However, there remains a clear need for a general theory, as we will finally demonstrate within the context of thermodynamics.