/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`
$ρ_{i}$
`E`		$υ$

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)
$ρ_{i}$	Initial density (Real)	$[\frac{k g}{m^{3}}]$
`E`	Young's modulus (Real)	$[Pa]$
$υ$	Poisson's ratio (Real)

Example (Elastic - Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/ELAST/1/1
Steel
#              RHO_I
             7.85E-9                   0
#                  E                  nu
              210000                  .3
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

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 ( $υ$ ). The shear modulus (G) can be computed using E and $ν$ , as:(1)
$G = \frac{E}{2 (1 + ν)}$
The stress-strain relationship can be represented as shown:(2)
$[\begin{matrix} ε_{11} \\ ε_{22} \\ ε_{33} \\ 2 ε_{23} \\ 2 ε_{31} \\ 2 ε_{12} \end{matrix}] = [\begin{matrix} ε_{11} \\ ε_{22} \\ ε_{33} \\ γ_{23} \\ γ_{31} \\ γ_{12} \end{matrix}] = \frac{1}{E} [\begin{matrix} 1 & - ν & - ν & 0 & 0 & 0 \\ - ν & 1 & - ν & 0 & 0 & 0 \\ - ν & - ν & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 2 (1 + ν) & 0 & 0 \\ 0 & 0 & 0 & 0 & 2 (1 + ν) & 0 \\ 0 & 0 & 0 & 0 & 0 & 2 (1 + ν) \end{matrix}] [\begin{matrix} σ_{11} \\ σ_{22} \\ σ_{33} \\ σ_{23} \\ σ_{31} \\ σ_{12} \end{matrix}]$
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 quasi-static 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.