*MAT_120 (GURSON)

LS-DYNA Input Interface KeywordDefines a nonlinear elasto-plastic based on the Gurson constitutive law, which is used to model visco-elastic-plastic strain rate dependent porous metals.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
MAT_120 or MAT_GURSON
`mat_ID`	$ρ_{i}$	`E`	`Nu`	`A`	`N`	`q1`	`q2`
`f`_c	`f`_I	$ε$ _N	`S`_N	`f`_N	`B`	`ATYP`	`f`_F
`EPS1`	`EPS2`	`EPS3`	`EPS4`	`EPS5`	`EPS6`	`EPS7`	`EPS8`
`ES1`	`ES2`	`ES3`	`ES4`	`ES5`	`ES6`	`ES7`	`ES8`
Blank line
`LCSS`	`LCFF`	`NUMINT`	`LCF0`	`LCFC`	`LCFN`

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer)
$ρ_{i}$	Initial density . (Real)	$[\frac{kg}{m^{3}}]$
`E`	Young's modulus. (Real)	$[Pa]$
`Nu`	Poisson's ratio. (Real)
`A`	Yield stress. (Real)	$[Pa]$
`N`	Hardening exponent (used only if `ATYP`=1 and `LCSS`=0). (Real)
`q1`, `q2`	Damage material parameters. (Real)
`f`_c	Critical void volume fraction at coalescence. (Real)
`f`_I	Initial void volume fraction. (Real)
$ε$ _N	Nucleated effective plastic strain. (Real)
`S`_N	Gaussian standard deviation. (Real)	$[Pa]$
`f`_N	Nucleated void volume fraction. (Real)
`B`	Hardening parameter (used only for `ATYP`=`2`). (Real)	$[Pa]$
`ATYP`	Hardening type = 0 Perfect plastic, $σ_{y} = A$ = 1 Power law, $σ_{y} = A \cdot {(\frac{ε_{p} + (\frac{A}{E})}{\frac{A}{E}})}^{\frac{1}{N}}$ = 2 Linear hardening, $σ_{y} = A + (\frac{E \cdot B}{E - B}) ε_{p}$ = 3 8 points curve defined with `EPS1` - `EPS8` and `ES1` - `ES8`. (Integer)
`f`_F	Critical void volume fraction at ductile fracture. (Real)
`EPS1` - `EPS8`	Plastic strain data points. (Real)
`ES1` - `ES8`	Yield stress data points. (Real)	$[Pa]$
`LCSS`	Stress versus plastic strain curve or table identifier. (Integer)	$[Pa]$
`LCFF`	Load curve ID defining critical void volume fraction at ductile fracture `f`_F as a function of element length. 2 (Integer)
`NUMINT`	Element failure rule. > 0 Number of integration points which must fail before the element is deleted. < 0 Percentage of integration points through the thickness which must fail before the element is deleted. (Integer)
`LCFI`	Load curve ID defining initial void volume fraction `f`_I as a function of element length. 2 (Integer)
`LCFC`	Load curve ID defining critical void volume fraction at coalescence `f`_c as a function of element length. 2 (Integer)
`LCFN`	Load curve ID defining nucleated void volume fraction `f`_N as a function of element length. 2 (Integer)

Comments

This keyword maps to /MAT/LAW52 (GURSON).
With the current version, only the first ordinate of the curve is used.
The option “_TITLE” can be added to the end of this keyword. When “_TITLE” is included, an extra 80 characters long line is added after the keyword input line which allows an entity title to be defined.