/MAT/LAW1 (ELAST)
Block Format Keyword This keyword defines an isotropic, linear elastic material using Hooke's law. This law represents a linear relationship between stress and strain. It is available for truss, beam (type 3 only), shell and solid elements.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW1/mat_ID/unit_ID or /MAT/ELAST/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  $\upsilon $ 
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) 
$\left[\frac{\text{k}\text{g}}{{\text{m}}^{3}}\right]$ 
E  Young's modulus (Real) 
$\left[\text{Pa}\right]$ 
$\upsilon $  Poisson's ratio (Real) 
Example (Elastic  Steel)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
Mg mm s
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/ELAST/1/1
Steel
# RHO_I
7.85E9 0
# E nu
210000 .3
#12345678910
#ENDDATA
/END
#12345678910
Comments
 This material law is used to model
purely elastic materials. The material stiffness is determined by only two values: the
Young's modulus (E), and Poisson's ratio (
$\upsilon $
). The shear modulus (G) can be computed using E and
$\nu $
, as:
(1) $$G=\frac{E}{2\left(1+\nu \right)}$$  The stressstrain relationship can be
represented as shown:
(2) $$\left[\begin{array}{c}{\epsilon}_{11}\\ {\epsilon}_{22}\\ {\epsilon}_{33}\\ 2{\epsilon}_{23}\\ 2{\epsilon}_{31}\\ 2{\epsilon}_{12}\end{array}\right]=\left[\begin{array}{c}{\epsilon}_{11}\\ {\epsilon}_{22}\\ {\epsilon}_{33}\\ {\gamma}_{23}\\ {\gamma}_{31}\\ {\gamma}_{12}\end{array}\right]=\frac{1}{E}\left[\begin{array}{cccccc}1& \nu & \nu & 0& 0& 0\\ \nu & 1& \nu & 0& 0& 0\\ \nu & \nu & 1& 0& 0& 0\\ 0& 0& 0& 2(1+\nu )& 0& 0\\ 0& 0& 0& 0& 2(1+\nu )& 0\\ 0& 0& 0& 0& 0& 2(1+\nu )\end{array}\right]\left[\begin{array}{c}{\sigma}_{11}\\ {\sigma}_{22}\\ {\sigma}_{33}\\ {\sigma}_{23}\\ {\sigma}_{31}\\ {\sigma}_{12}\end{array}\right]$$  The value of density is always used in explicit simulations and it may also be used in static implicit simulations to reach a better convergence in quasistatic analysis.
 Global integration approach is applied
to LAW1 and shell elements (/PROP/TYPE1 (SHELL)), when the number of
integration points through the shell thickness is different from NP=1
(membranes).Note: Failure models are not available in the case of global integration. LAW2 and LAW27 with very high yield stress may be used as a substitution to LAW1 in these cases.