/MAT/LAW15 (CHANG)
Block Format Keyword This law is used to model composite shell elements, similar to LAW25. The plastic behavior is based on the TsaiWu criteria (/MAT/LAW25 (COMPSH) for TsaiWu description) and failure is based on the ChangChang failure criterion is used.
It is recommended to use material LAW25 in combination with a separate ChangChang failure criteria (/MAT/LAW25 with /FAIL/CHANG keywords), instead of material LAW15.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW15/mat_ID/unit_ID or /MAT/CHANG/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E_{11}  E_{22}  ${\nu}_{12}$  
G_{12}  G_{23}  G_{31}  
b  n  f_{max}  
${W}_{p}^{\text{max}}$  ${W}_{p}^{\mathit{ref}}$  Ioff  
${\sigma}_{1y}^{t}$  ${\sigma}_{2y}^{t}$  ${\sigma}_{1y}^{c}$  ${\sigma}_{2y}^{c}$  α  
${\sigma}_{12y}^{c}$  ${\sigma}_{12y}^{t}$  c  ${\dot{\epsilon}}_{0}$  ICC  
$\beta $  ${\tau}_{\mathrm{max}}$  S_{1}  S_{2}  S_{12}  
F_{smooth}  F_{cut}  C_{1}  C_{2} 
Definitions
Field  Contents  SI Unit Example 

mat_ID  Material
identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Integer, maximum 10 digits) 

mat_title  Material
title. (Character, maximum 100 characters) 

${\rho}_{i}$  Initial
density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
E_{11}  Young's modulus in
direction 1. (Real) 
$\left[\text{Pa}\right]$ 
E_{22}  Young's modulus in
direction 2. (Real) 
$\left[\text{Pa}\right]$ 
${\nu}_{12}$  Poisson's
ratio. (Real) 

G_{12}  Shear
modulus. (Real) 
$\left[\text{Pa}\right]$ 
G_{23}  Shear
modulus. (Real) 
$\left[\text{Pa}\right]$ 
G_{31}_{1}  Shear
modulus. (Real) 
$\left[\text{Pa}\right]$ 
b  Hardening
parameter. (Real) 

n  Hardening
exponent. Default = 1.0 (Real) 

fmax  Maximum value of yield
function. 2 Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
${W}_{p}^{\text{max}}$  Maximum plastic energy per
volume unit. Default = 10^{30} (Real) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$ 
${W}_{p}^{\mathit{ref}}$  Reference plastic energy
per volume unit. Default = 1.0 (Real) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$ 
Ioff  Total element failure
criteria. 4
(Integer) 

${\sigma}_{1y}^{t}$  Composite yield stress in
tension in direction 1. 2 (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{2y}^{t}$  Composite yield stress in
tension in direction 2. (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{1y}^{c}$  Composite yield stress in
compression in direction 1. (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{2y}^{c}$  Composite yield stress in
compression in direction 2. (Real) 
$\left[\text{Pa}\right]$ 
α  F12
reduction factor. 2 Default set to 1.0 (Real) 

${\sigma}_{12y}^{c}$  Yield stress in shear and
strain rate compression in direction 12. (Real) 
$\left[\text{Pa}\right]$ 
${\sigma}_{12y}^{t}$  Yield stress in shear and
strain rate tension in direction 12. (Real) 
$\left[\text{Pa}\right]$ 
c  Yield stress in shear and
strain rate coefficient. 2
(Real) 

${\dot{\epsilon}}_{0}$  Yield stress in shear and
strain rate reference. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
ICC  Strain rate computation
flag. 2
(Integer) 

$\beta $  Shear scaling factor.
1 (Real) 

${\tau}_{\mathrm{max}}$  Time relaxation. 3 Default = 10^{30} (Real) 
$\left[\text{s}\right]$ 
S_{1}  Longitudinal tensile
strength. 1 Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
S_{2}  Transverse tensile
strength. Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
S_{12}  Shear strength. Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
F_{smooth}  Smooth strain rate option flag.
(Integer) 

F_{cut}  Cutoff frequency for
strain rate filtering. Default = 10^{30} (Real) 
$\text{[Hz]}$ 
C_{1}  Longitudinal compressive
strength. 1 Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
C_{2}  Transverse compressive
strength. Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
Example (Carbon)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
kg mm ms
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW15/1/1
Carbon
# RHO_I
1.8E6 0
# E11 E22 nu12
41 3.3 .3
# G12 G23 G31
5.2 1.3 1.3
# b n fmax
8E6 1 100000
# Wpmax Wpref Ioff
100000 0 0
# sigma_1yt sigma_2yt sigma_1yc sigma_2yc alpha
.786 .1566 .786 .1566 0
# sigma_12yc sigma_12yt c Eps_dot_0 ICC
.0655 .0655 0 0 0
# beta Tmax S1 S2 S12
1 .01 0 0 0
# Fsmooth Fcut C1 C12
0 0 0 0
#12345678910
#ENDDATA
/END
#12345678910
Comments
 ChangChang failure criteriaSix material parameters are used in the ChangChang failure criteria to describe the two different failure behaviors.
 For fiber breakage, the failure criteria is:
 Tensile fiber mode
${\sigma}_{11}>0$
(1) $${e}_{f}^{2}={\left(\frac{{\sigma}_{11}}{{S}_{1}}\right)}^{2}+\beta {\left(\frac{{\sigma}_{12}}{{S}_{12}}\right)}^{2}1.0$$$\begin{array}{l}\ge 0\mathit{failed}\\ <0\mathit{elastic}\mathit{plastic}\end{array}$  Compressive fiber mode
${\sigma}_{11}<0$
(2) $${e}_{c}^{2}={\left(\frac{{\sigma}_{11}}{{C}_{1}}\right)}^{2}1.0$$$\begin{array}{l}\ge 0\mathit{failed}\\ <0\mathit{elastic}\mathit{plastic}\end{array}$
 Tensile fiber mode
${\sigma}_{11}>0$
 For matrix cracking, the failure criteria is:
 Tensile fiber mode
${\sigma}_{22}>0$
(3) $${e}_{m}^{2}={\left(\frac{{\sigma}_{22}}{{S}_{2}}\right)}^{2}+\beta {\left(\frac{{\sigma}_{12}}{{S}_{12}}\right)}^{2}1.0$$$\begin{array}{l}\ge 0\mathit{failed}\\ <0\mathit{elastic}\mathit{plastic}\end{array}$  Compressive matrix mode ${\sigma}_{22}<0$
(4) $${e}_{d}^{2}={\left(\frac{{\sigma}_{22}}{2{S}_{12}}\right)}^{2}+\left[{\left(\frac{{C}_{2}}{2{S}_{12}}\right)}^{2}1\right]\frac{{\sigma}_{22}}{{C}_{2}}+{\left(\frac{{\sigma}_{12}}{{S}_{12}}\right)}^{2}1.0$$$\begin{array}{l}\ge 0\mathit{failed}\\ <0\mathit{elastic}\mathit{plastic}\end{array}$  Tensile fiber mode
${\sigma}_{22}>0$
 For fiber breakage, the failure criteria is:
 Before failed (damage parameter ${e}_{f}{}^{2},{e}_{c}{}^{2},{e}_{m}{}^{2},{e}_{d}{}^{2}$ is less than 0), material is in elastic–plastic phase. The plastic behavior is based on the TSAIWU criteria (see TsaiWu Formulation (Iform =0) for TsaiWu criterion description).
 After failed (damage parameter
${e}_{f}{}^{2},{e}_{c}{}^{2},{e}_{m}{}^{2},{e}_{d}{}^{2}$
is greater than or equal to 0), the stresses are
decreased by using an exponential function to avoid numerical instabilities.A relaxation technique is used by gradually decreasing the stress.
(5) $$\sigma (t)=\mathrm{f}(t)\cdot {\sigma}_{d}({t}_{r})$$With function of relaxation:
$\mathrm{f}(t)=\mathrm{exp}\left(\frac{t{t}_{r}}{{\tau}_{\mathrm{max}}}\right)$ and $t\ge {t}_{r}$
Where, $t$
 Time
 ${t}_{r}$
 Start time of relaxation when the damage criteria is assumed
 ${\tau}_{\mathrm{max}}$
 Time of dynamic relaxation
 ${\sigma}_{d}({t}_{r})$
 Stress components at the beginning of damage
 If a shell has several layers with one material per layer (different materials, different I_{off}), the I_{off} used is the one which is associated to the shell in the shell element definition.