*MAT_015 (JOHNSON_COOK)

LS-DYNA Input Interface KeywordThis model expresses material stress as a function of strain, strain rate, temperature dependency and plastic strain failure criterion.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
MAT_015 or MAT_JOHNSON_COOK
`mat_ID`	$ρ_{i}$		`E`	`v`
`a`	`b`	`n`	`c`	`m`	`Tmelt`	`Tr`	${\dot{ε}}_{0}$
`CP`				`D1`	`D2`	`D3`	`D4`
`D5`		`EROD`	`EFMIN`	`NUINT`

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)	$[Pa]$
`v`	Poisson’s ratio (Real)
`a`	Yield stress (Real)	$[Pa]$
`b`	Plastic hardening parameter (Real)	$[Pa]$
`n`	Plastic hardening exponent (Real)
`c`	Strain rate coefficient (Real)
`m`	Temperature exponent Default = 1.00 (Real)
`Tmelt`	Melting temperature Default 10³⁰ (Real)	$[K]$
`Tr`	Reference temperature. Default = 298 K (Real)	$[K]$
${\dot{ε}}_{0}$	Reference strain rate (Real)	$[\frac{1}{s}]$
`CP`	Specific heat capacity (Real)	$[\frac{J}{kg \cdot K}]$
`D1`	1st parameter or Johnson failure model (Real)
`D2`	2nd parameter or Johnson failure model (Real)
`D3`	3rd parameter or Johnson failure model (Real)
`D4`	4th parameter or Johnson failure model (Real)
`D5`	5th parameter or Johnson failure model (Real)
`EROD`	Solid element erosion behavior = 0 Solid element is deleted when 1 integration reaches the failure criteria. ≠ 0 For each integration point, the deviatoric stress tensor vanishes when the failure criteria is reached.
`EFMIN`	Lower plastic strain failure model (Real)
`NUINT`	Number of integration point for shell element erosion (Real)

Comments

This keyword maps to /MAT/LAW2 (PLAS_JOHNS) and /FAIL/JOHNSON.
The option “_TITLE” can be added to the end of this keyword. When “_TITLE” is included, an extra 80 character long line is added after the keyword input line which allows an entity title to be defined.