uniaxial¶
NEML material models are strain-controlled and 3D. Degenerating this response to plane strain is trivial – simply pass in zeros in the appropriate strain components. However, another very useful stress state is strain-controlled uniaxial stress. This is the stress state in many common experimental tests, for example standard tension tests. The stress state in these conditions is:
![\bm{\sigma}=
\left[\begin{array}{ccc}
\sigma & 0 & 0\\
0 & 0 & 0\\
0 & 0 & 0
\end{array}\right]](_images/math/84d4ab6777c2112aad613b6e003723c39b14e05b.png)
where 
is the unknown uniaxial stress. The strain state is
![\bm{\varepsilon} =
\left[\begin{array}{ccc}
\varepsilon & \varepsilon_{12} & \varepsilon_{13}\\
\varepsilon_{12} & \varepsilon_{22} & \varepsilon_{23}\\
\varepsilon_{13} & \varepsilon_{23} & \varepsilon_{33}
\end{array}\right]](_images/math/29f30df625d5ab8b1299930447584a3ec15b42d3.png)
where 
is the known, controlled input strain and the
remaining strain components are unknowns.
The neml axisym module solves a system of nonlinear equations to impose this state of strain and stress on a standard, 3D NEML material model. The module returns the uniaxial stress, the history, the stored energy and dissipated work, along with the new, uniaxial algorithmic tangent
