ElasticPlastic Orthotropic Composite Solids
The material LAW14 (COMPSO) in Radioss allows to simulate orthotropic elasticity, TsaiWu plasticity with damage, brittle rupture and strain rate effects. The constitutive law applies to only one layer of lamina. Therefore, each layer needs to be modeled by a solid mesh. A layer is characterized by one direction of the fiber or material. The overall behavior is assumed to be elastoplastic orthotropic.
For the case of unidirectional orthotropy (i.e. $${E}_{33}={E}_{22}$$ and $${G}_{31}={G}_{12}$$) the material LAW53 in Radioss allows to simulate an orthotropic elasticplastic behavior by using a modified TsaiWu criteria.
Linear Elasticity
 Transform the lamina stress, $${\sigma}_{ij}\left(t\right)$$, and strain rate, $${d}_{ij}$$, from global reference frame to fiber reference frame.
 Compute lamina stress at time $$t+\text{\Delta}t$$ by explicit time integration:
(1) $${\sigma}_{ij}\left(t+\text{\Delta}t\right)={\sigma}_{ij}\left(t\right)+{D}_{ijkl}\text{\hspace{0.05em}}{d}_{kl}\text{\hspace{0.05em}}\text{\Delta}t$$  Transform the lamina stress, $${\sigma}_{ij}\left(t+\text{\Delta}t\right)$$, back to global reference frame.
 $${E}_{ij}$$
 Young's modulus
 $${G}_{ij}$$
 Shear modulus
 ${\nu}_{ij}$
 Poisson's ratios
 $${\gamma}_{ij}$$
 Strain components due to the distortion
Orthotropic Plasticity
with:
${F}_{i}=\frac{1}{{\sigma}_{iy}^{c}}+\frac{1}{{\sigma}_{iy}^{t}}$ ($$i$$=1,2,3);
${F}_{11}=\frac{1}{{\sigma}_{1y}^{c}{\sigma}_{1y}^{t}}$; ${F}_{22}=\frac{1}{{\sigma}_{2y}^{c}{\sigma}_{2y}^{t}}$; ${F}_{33}=\frac{1}{{\sigma}_{3y}^{c}{\sigma}_{3y}^{t}}$;
${F}_{44}=\frac{1}{{\sigma}_{12y}^{c}{\sigma}_{12y}^{t}}$; ${F}_{55}=\frac{1}{{\sigma}_{23y}^{c}{\sigma}_{23y}^{t}}$; ${F}_{66}=\frac{1}{{\sigma}_{31y}^{c}{\sigma}_{31y}^{t}}$;
$${F}_{12}=\frac{1}{2}\sqrt{\left({F}_{11}{F}_{22}\right)}$$ ; $${F}_{23}=\frac{1}{2}{F}_{22}$$
 $${W}_{p}$$
 Plastic work
 $$B$$
 Hardening parameter
 $$n$$
 Hardening exponent
 $$c$$
 Strain rate coefficient
If the maximum value is reached the material is failed.
(a) Strain rate effect on ${\sigma}_{\mathrm{max}}$  (b) No strain rate effect on ${\sigma}_{\mathrm{max}}$ 



$$\sigma ={\sigma}_{y}\left(1+c.1\text{n}\left(\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{0}}\right)\right)$$ $${\sigma}_{\mathrm{max}}={\sigma}_{\mathrm{max}}^{0}\left(1+c.1\text{n}\left(\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{0}}\right)\right)$$ $${f}_{\mathrm{max}}={\left(\frac{{\sigma}_{\mathrm{max}}}{{\sigma}_{y}}\right)}^{2}$$ 
$$\sigma ={\sigma}_{y}\left(1+c.1\text{n}\left(\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{0}}\right)\right)$$ $${\sigma}_{\mathrm{max}}={\sigma}_{\mathrm{max}}^{0}$$ 