MATX02

Bulk Data Entry Defines additional material properties for Johnson-Cooke elastic-plastic material for geometric nonlinear analysis. This is an elasto-plastic law with strain rate and temperature effects.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MATX02	`MID`	`A`	`B`	`N`	`EPSMAX`	`SIGMAX`	`C`	`DEPS0`
	`ICC`	`FSMOOTH`	`F`	`M`	`T`	`RCP`

Example

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MAT1	102	60.4		0.33	2.70E-06
MATX02	102	0.09026	0.22313	0.374618	100.0	0.175

Definitions

Field	Contents	SI Unit Example
`MID`	Material ID of the associated MAT1. 1 No default (Integer > 0)
`A`	Plasticity yield stress. (Real > 0)
`B`	Plasticity hardening parameter. (Real ≥ 0)
`N`	Plasticity hardening exponent. Default = 1.0 (Real ≤ 1.0)
`EPSMAX`	Failure plastic strain $ε$ $ε_{\max}$ Default = 10³⁰ (Real > 0)
`SIGMAX`	Maximum plastic stress $σ_{\max 0}$ Default = 10³⁰ (Real > 0)
`C`	Strain rate coefficient. If zero, there is no strain rate effect. Default = 0.0 (Real)
`DEPS0`	Reference strain rate ${\dot{ε}}_{0}$ . Default = 0.0 (Real) If `DESPS` ≤ `DESPS0`, no strain rate effect.
`ICC`	Strain rate dependency of $σ_{\max 0}$ flag. 5 OFF ON (Default)
`FSMOOTH`	Strain rate smoothing flag. OFF (Default) ON
`F`	Cutoff frequency for strain rate filtering. Only for shell and solid elements. Default = 10³⁰ (Real ≥ 0)
`M`	Temperature exponent. Default = 0.0 (Real)
`T`	Melting temperature. Default = 10³⁰ (Real > 0)
`RCP`	Specific heat per unit of volume. Default = 0.0 (Real ≥ 0)

Comments

The material identification number must be that of an existing MAT1 Bulk Data Entry. Only one MATXi material extension can be associated with a particular MAT1.
MATX02 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS=EXPDYN. It is ignored for all other subcases.
This is an elastic-plastic law with strain rate and thermal effects. It follows:(1)
$σ = (a + b ε_{p}^{n}) (1 + c In \frac{\dot{ε}}{{\dot{ε}}_{0}}) (1 - T^{* m})$

Where,(2)
$T * = \frac{T - T_{0}}{T_{melt} - T_{0}}$

Where,

$ε_{p}$

Plastic strain

$\dot{ε}$

Strain rate

$T$

Temperature (in Kelvin)
If the plastic strain reaches EPSMAX, shell elements are deleted. Solid elements are not deleted, but the deviatoric stress is set to zero.

ICC controls the strain rate effect.

$\begin{array}{l} σ = σ_{y} (1 + cIn (\frac{\dot{ε}}{{\dot{ε}}_{0}})) \\ σ_{\max} = σ_{\max 0} (1 + cIn \frac{\dot{ε}}{{\dot{ε}}_{0}}) \end{array}$	$\begin{array}{l} σ = σ_{y} (1 + cIn (\frac{\dot{ε}}{{\dot{ε}}_{0}})) \\ σ_{\max} = σ_{\max 0} \end{array}$

Figure 1.

No strain rate effects are considered in rod elements.
Strain rate filtering is used to smooth strain rates. The input F is available only for shell and solid elements.
To take into account the temperature effect, strain rate dependence must be activated. If the temperature exponent M=0; there is no temperature effect. No temperature effect is considered on rod, bar, and beam elements.
The temperature is computed assuming adiabatic conditions:(3)
$T = T_{i} + \frac{E_{int}}{ρ C_{p} (Volume)}$

Where, E is the internal energy.

If $ρ C_{p}$ = 0, the temperature is constant $T = T {}_{i}$ .
This card is represented as an extension to a MAT1 material in HyperMesh.