FAQ 003411 EN

5 August 2019

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

The material model according to Tsai-Wu unifies plastic with orthotropic properties. This way, you can enter special modelings of materials with anisotropic characteristics such as plastics or timber. When the material is plasticized, stresses remain constant. A redistribution is carried out according to the stiffnesses available in the individual directions. The elastic zone corresponds to the material model Orthotropic - 3D. For the plastic zone, the yielding according to Tsai-Wu applies:

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

with:

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

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

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

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

The yielding condition can be thought of as an elliptical surface in a six-dimensional space of tension.
If one of the three stress components is applied as a constant value, the surface can be projected onto a three-dimensional stress space. Projection of yielding surfaces for normal stresses according to Tsai-Wu If the value for fy (σ) is smaller than 1, the stresses lie within the elastic range. The plastic zone is reached as soon as fy (σ) = 1; values greater than 1 are not allowed. The model behavior is ideal-plastic, which means no stiffening takes place.