# How does the "Orthotropic Plastic" material model work in RFEM?

The material model according to Tsai-Wu unifies the plastic with the orthotropic properties. In this way, it is possible to specifically model the materials with anisotropic properties, such as plastics or timber. If the material is plastified, the stresses remain constant. The redistribution is carried out according to the stiffnesses available in the individual directions. The elastic area corresponds to the Orthotropic Elastic - 3D material model. For the plastic area, the yielding according to Tsai-Wu applies:

${\text{f}}_{\mathrm{crit}}\left(\mathrm\delta\right)=\frac1{\mathrm C}\left[\frac{\left({\mathrm\delta}_{\mathrm x}-{\mathrm\delta}_{\mathrm x,0}\right)^2}{{\mathrm f}_{\mathrm t,\mathrm x}{\mathrm f}_{\mathrm c,\mathrm x}}+\frac{\left({\mathrm\delta}_{\mathrm y}-{\mathrm\delta}_{\mathrm y,0}\right)^2}{{\mathrm f}_{\mathrm t,\mathrm y}{\mathrm f}_{\mathrm c,\mathrm y}}+\frac{\left({\mathrm\delta}_{\mathrm z}-{\mathrm\delta}_{\mathrm z,0}\right)^2}{{\mathrm f}_{\mathrm t,\mathrm z}{\mathrm f}_{\mathrm c,\mathrm z}}+\frac{{\mathrm\tau}_{\mathrm{yz}}^2}{{\mathrm f}_{\mathrm v,\mathrm{yz}}^2}+\frac{{\mathrm\tau}_{\mathrm{xz}}^2}{{\mathrm f}_{\mathrm v,\mathrm{xz}}^2}+\frac{{\mathrm\tau}_{\mathrm{xy}}^2}{{\mathrm f}_{\mathrm v,\mathrm{xy}}^2}\right]$

where:

${\mathrm\delta}_{\mathrm x,0}=\frac{{\mathrm f}_{\mathrm t,\mathrm x}-{\mathrm f}_{\mathrm c,\mathrm x}}2$

${\mathrm\delta}_{\mathrm y,0}=\frac{{\mathrm f}_{\mathrm t,\mathrm y}-{\mathrm f}_{\mathrm c,\mathrm y}}2$

${\mathrm\delta}_{\mathrm z,0}=\frac{{\mathrm f}_{\mathrm t,\mathrm z}-{\mathrm f}_{\mathrm c,\mathrm z}}2$

$\mathrm C=1+\left[\frac1{{\mathrm f}_{\mathrm t,\mathrm x}}+\frac1{{\mathrm f}_{\mathrm c,\mathrm x}}\right]^2\frac{{\mathrm E}_{\mathrm x}{\mathrm E}_{\mathrm p,\mathrm x}}{{\mathrm E}_{\mathrm x}-{\mathrm E}_{\mathrm p,\mathrm x}}\mathrm\alpha+\frac{{\mathrm\delta}_{\mathrm x,0}^2}{{\mathrm f}_{\mathrm t,\mathrm x}{\mathrm f}_{\mathrm c,\mathrm x}}+\frac{{\mathrm\delta}_{\mathrm y,0}^2}{{\mathrm f}_{\mathrm t,\mathrm y}{\mathrm f}_{\mathrm c,\mathrm y}}+\frac{{\mathrm\delta}_{\mathrm z,0}^2}{{\mathrm f}_{\mathrm t,\mathrm z}{\mathrm f}_{\mathrm c,\mathrm y}}$

You can imagine the yield criterion as an elliptical surface in a six-dimensional stress space.
If one of the three stress components is applied as a constant value, the surface can be projected onto a three-dimensional stress space. The projection of yield surfaces for normal stresses according to Tsai‑Wu: if the value for fy (σ) is smaller than 1, the stresses rest within the elastic area. The plastic area is reached as soon as fy (σ) = 1; the values greater than 1 are not allowed. The model behavior is ideal-plastic, which means there is no stiffening.