/MAT/LAW3 (HYDPLA)

Block Format Keyword This law represents an isotropic elasto-plastic material using the Johnson-Cook material model.

This model expresses material stress as a function of strain and may account for the nonlinear dependence between pressure and volumetric strain when corresponding equation of state is specified. A built-in failure criterion based on the maximum plastic strain is available. This material law is compatible with solid elements only.

Format


(1)	(3)	(5)	(7)	(9)
/MAT/LAW3/`mat_ID`/`unit_ID` or /MAT/HYDPLA/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$	$ρ_{0}$
`E`	$ν$
`a`	`b`	`n`	$ε_{p}^{m a x}$	$σ_{\max}$
`P`_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)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
$ρ_{0}$	Reference density used in E.O.S (equation of state). Default = $ρ_{0} = ρ_{i}$ (Real)	$[\frac{kg}{m^{3}}]$
`E`	Young's modulus. (Real)	$[Pa]$
$ν$	Poisson's ratio. (Real)
`a`	Plastic yield stress. (Real)	$[Pa]$
`b`	Plastic hardening parameter. (Real)	$[Pa]$
`n`	Plastic hardening exponent. (Real)
$ε_{p}^{m a x}$	Failure plastic strain. Default = 10³⁰ (Real)
$σ_{\max}$	Maximum stress. Default = 10³⁰ (Real)	$[Pa]$
`P`_min	Cutoff minimum pressure ( < 0 ). Default = -10³⁰ (Real)	$[Pa]$

▸Example (Aluminum)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  g                  cm                 mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYDPLA/1/1
Aluminum
#              RHO_I               RHO_0
                 2.8                   0
#                  E                  nu
              .72352                 .33
#                  a                   b                   n             eps_max           sigma_max
               .0024               .0042                  .8                   9               .0068
#               Pmin                 Psh
               -.005
/EOS/TILLOTSON/1/1
Aluminum
#                 C1                  C2                   A                   B
                .752                 .65                  .5                1.63
#                 ER                  ES                  VS                  E0               RHO_0
                .135                .081                 1.1                   0                   0
#              ALPHA                BETA
                   5                   5
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

In this model, the material behaves as a linear-elastic material when the equivalent stress is lower than the plastic yield stress. For higher stress values, the material behavior is plastic and the stress is calculated as:
$σ = (a + b ε_{p}^{n})$
Where, ${\bar{ε}}_{p}$ is the plastic strain.
The plastic yield stress should always be greater than zero. To model pure elastic behavior, the plastic yield stress will be set to 10³⁰.
By default, the hydrostatic pressure is linearly proportional to volumetric strain:
$P = K μ$
Where, $K = \frac{E}{3 (1 - 2 ν)}$ is the bulk modulus and $μ = \frac{ρ}{ρ_{0}} - 1$ is the volumetic strain.
An additional Equation of State (Equation of State) card can refer to this material in order to incorporate a nonlinear dependency between hydrostatic pressure and volumetric strain. The yield stress should be strictly positive.
When ${\bar{ε}}_{p}$ attains (or exceeds) the value of $ε_{p}^{m a x}$ (for tension, compression or shear), in one integration point, the solid element are deleted.