/MAT/LAW10 (DPRAG1)
Block Format Keyword This law, based on an extended DruckerPrager yield criteria, is used to model materials with internal friction such as rockconcrete.
The yield criteria is pressure dependent. To compute the pressure an equation of
state must be provided (such as /EOS/COMPACTION). This law is
compatible only with solid elements.
Important: Starting in version
2019.1, the equation of state (EOS) parameters were removed from this material
law. Any model using the old format that includes the EOS parameters will be
converted during import into the updated material law format with an associated
/EOS/COMPACTION.
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}  
$\text{\Delta}{P}_{\mathrm{min}}$ 
Definition
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  Young's
modulus. (Real) 
$\left[\text{Pa}\right]$ 
$\nu $  Poisson's
ratio. (Real) 

A_{0}  Yield criteria
coefficient. (Real) 
$\left[\text{P}{\text{a}}^{2}\right]$ 
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) 
$\left[\text{P}{\text{a}}^{2}\right]$ 
$\text{\Delta}{P}_{\mathrm{min}}$  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
Concrete 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 DruckerPrager
yield criterion has a linear pressure dependency.Radioss is using the extended DruckerPrager yield criteria whose pressure dependency is nonlinear.
 Extended DruckerPrager
yield criteria can be compared with MohrCoulomb criteria.An extended DruckerPrager 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:$${A}_{0}=k{\left(c,\varphi \right)}^{2}$$ $${A}_{1}=6k\left(c,\varphi \right)\times \alpha \left(\varphi \right)$$ $${A}_{2}=9\alpha {\left(\varphi \right)}^{2}$$ Modeling Type
 Parameters
 Circumscribed DruckerPrager 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 DruckerPrager 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 DruckerPrager 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.
 Starter checks the yield parameters A_{0}, A_{1}, and A_{2} and warns you in case of an unexpected situation.