/MAT/LAW40 (KELVINMAX)

Block Format Keyword This law describes the generalized Maxwell-Kelvin material. This law can only be used with solid elements.

Format


(1)	(3)	(5)	(7)	(9)
/MAT/LAW40/`mat_ID`/`unit_ID` or /MAT/KELVINMAX/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`K`	$G_{\infty}$	`A`_stass	`B`_stass	`K`_vm
`G`₁	`G`₂	`G`₃	`G`₄	`G`₅
$β_{1}$	$β_{2}$	$β_{3}$	$β_{4}$	$β_{5}$

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)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
`K`	Bulk modulus. (Real)	$[Pa]$
$G_{\infty}$	Long time shear modulus. (Real)	$[Pa]$
`A`_stass	Stassi A coefficient. (Real)	$[Pa]$
`B`_stass	Stassi B coefficient. (Real)	$[Pa]$
`Kvm`	von Mises coefficient. (Real)
`G`₁	Shear modulus 1. (Real)	$[Pa]$
`G`₂	Shear modulus 2. (Real)	$[Pa]$
`G`₃	Shear modulus 3. (Real)	$[Pa]$
`G`₄	Shear modulus 4. (Real)	$[Pa]$
`G`₅	Shear modulus 5. (Real)	$[Pa]$
$β_{1}$	Time decay constant 1. (Real)
$β_{2}$	Time decay constant 2. (Real)
$β_{3}$	Time decay constant 3. (Real)
$β_{4}$	Time decay constant 4. (Real)
$β_{5}$	Time decay constant 5. (Real)

Example (Elastic Rubber)


#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/KELVINMAX/1/1
LAW40 elastic rubber
#              RHO_I
                1E-9
#                  K               G_inf              Astass              Bstass                 Kvm
                8.97                   3                   0                   0                   0
#                 G1                  G2                  G3                  G4                  G5
                   0                   0                   0                   0                   0
#              BETA1               BETA2               BETA3               BETA4               BETA5
                   0                   0                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

Shear modulus is computed using the following equation:
$G (t) = G_{\infty} + \sum_{1}^{5} G_{i} e^{- β_{i} t}$
with $β_{i} = \frac{1}{τ_{i}}$
Where $τ_{i}$ is the relaxation time.
Variables K_vm, A_stass, and B_stass are not used in this material law; except for some output in user variables.
Poisson number "NU" ( $ν$ ) is calculated automatically with bulk modulus K and initial shear modulus G at time= 0, as:
$ν = \frac{3 K - 2 G}{2 (3 K + G)}$
Where, initial shear modulus $G = G_{\infty} + G_{1} + G_{2} + G_{3} + G_{4} + G_{5}$ .
Poisson number "NU" ( $ν$ ) must be positive and $0 < ν < 0.5$ .