/MAT/LAW10 (DPRAG1)
Block Format Keyword This law, based on an extended DrückerPrager yield criteria, is used to model materials with internal friction such as rockconcrete.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW10/mat_ID/unit_ID or /MAT/DPRAG1/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  $\nu $  
A_{0}  A_{1}  A_{2}  A_{max}  
$\text{\Delta}{P}_{\mathrm{min}}$ 
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) 
$\left[\frac{\text{kg}}{{\text{m}}^{3}}\right]$ 
E  Young's
modulus. (Real) 
$\left[\text{Pa}\right]$ 
$\nu $  Poisson's
ratio. (Real) 

A_{0}  Yield criteria
coefficient. (Real) 
$\left[{\text{Pa}}^{\text{2}}\right]$ 
A_{1}  Yield criteria
coefficient. (Real) 
$\left[\text{Pa}\right]$ 
A_{2}  Yield criteria
coefficient. (Real) 

A_{max}  Yield criteria limit (von
Mises limit). (Real) 
$\left[{\text{Pa}}^{\text{2}}\right]$ 
$\text{\Delta}{P}_{\mathrm{min}}$  Minimum
pressure. Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
Example (Concrete)
#RADIOSS STARTER
/UNIT/1
unit for mat
g cm mus
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW10/1/1
Concrete
# RHO_I
2.4
# E Nu
.576 .25
# A0 A1 A2 Amax
9.72E10 4.32E5 .48 .013
# P_min
1E20
/EOS/COMPACTION/1/1
Concreate EOS
# C0 C1 C2 C3
0.0 0.256 0.256 1
# MUMIN MUMAX BUNL
0.0 0.44 0.115
# PSH RHO0
0 2.40
#12345678910
#ENDDATA
Comments
 Original DrückerPrager
yield criterion has a linear pressure dependency.
Radioss is using the extended DrückerPrager yield criteria whose pressure dependency is nonlinear.
 Extended DrückerPrager
yield criteria can be compared with MohrCoulomb criteria.
An extended DrückerPrager yield criterion can be fitted from MohrCoulomb parameters:
 $c$
 Cohesion parameter
 $\varphi $
 Angle of internal friction
For this purpose, parameters ${A}_{0},{A}_{1},{A}_{2}$ must be defined as:(1) ${A}_{0}=k{\left(c,\varphi \right)}^{2}$
${A}_{1}=6k\left(c,\varphi \right)\times \alpha \left(\varphi \right)$
${A}_{2}=9\alpha {\left(\varphi \right)}^{2}$
 Modeling Type
 Parameters
 Circumscribed DrückerPrager criteria
 $\begin{array}{l}k=\frac{6c\times \mathrm{cos}(\varphi )}{\sqrt{3}\left(3\mathrm{sin}(\varphi )\right)}\\ \alpha =\frac{2\mathrm{sin}(\varphi )}{\sqrt{3}\left(3\mathrm{sin}(\varphi )\right)}\end{array}$
 Middle Circle
 $\begin{array}{l}k=\frac{6c\times \mathrm{cos}(\varphi )}{\sqrt{3}\left(3+\mathrm{sin}(\varphi )\right)}\\ \alpha =\frac{2\mathrm{sin}(\varphi )}{\sqrt{3}\left(3+\mathrm{sin}(\varphi )\right)}\end{array}$
 Inscribed DrückerPrager criteria
 $\begin{array}{l}k=\frac{3c\times \mathrm{cos}(\varphi )}{\sqrt{9+3{\mathrm{sin}}^{2}(\varphi )}}\\ \alpha =\frac{\mathrm{sin}(\varphi )}{\sqrt{9+3{\mathrm{sin}}^{2}(\varphi )}}\end{array}$
 /MAT/LAW21 is also based on an extended DrückerPrager yield criteria but pressure evolution can be described with user functions.
 Young's modulus E and Poisson’s ratio $\nu $ are used to determined shear modulus G which is required for sound speed calculation in solid materials.