  A new model for elucidating the mathematical foundation of plasticity yield
criteria is proposed. The proposed ansatz uses differential geometry and group
theory concepts in addition to elementary hypotheses based on well-established
experimental evidence. Its theoretical development involves the analysis of
tensor functions and provides a series expansion which allows the functional
stress-dependence of plasticity yield criteria to be predicted. The theoretical
framework for the model includes a series of spatial coefficients that provide
a more flexible theory for in-depth examination of symmetry and anisotropy in
compact solid materials. It describes the classical yield criteria (like those
of Tresca, Von Mises, Hosford, Hill, etc) and accurately describes the
anomalous behaviour of metals such as aluminium, which was elucidated by Hill
(1979). Further, absolutely new instances of stress-dependence are predicted;
this makes it highly useful for fitting experimental data with a view to
studying the phenomena behind plasticity.
