# /MAT/LAW103 (HENSEL-SPITTEL)

Block Format Keyword This law represents an isotropic elastic-plastic material at high temperature using Hensel-Spittel yield stress formula. The yield stress is a function of strain, strain rate and temperature. This material law can be used with an equation of state /EOS.

This material is often used in hot forging simulations. The law parameters are valid only for a given range of temperature and strain rate. This material law is compatible with solid elements only.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW103/mat_ID/unit_ID or /MAT/HENSEL-SPITTEL/mat_ID/unit_ID
mat_title
${\rho }_{i}$ ${\rho }_{0}$
E $\nu$
A0 m1 m2 m3 m4
m5 m7
Fsmooth Fcut ${\epsilon }_{0}$ Pmin
$\rho {C}_{p}$ T0 $\eta$

## Definitions

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)

${\rho }_{i}$ Initial density.

(Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
${\rho }_{0}$ Reference density used in the default equation of state.

Default = ${\rho }_{i}$ (Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
E Initial Young's modulus.

(Real)

$\left[\text{Pa}\right]$
$\nu$ Poisson's ratio.

(Real)

A0 Stress parameter.

(Real)

$\left[\text{Pa}\right]$
m1 Material parameter 1.

(Real)

m2 Material parameter 2.

(Real)

m3 Material parameter 3.

(Real)

m4 Material parameter 4.

(Real)

m5 Material parameter 5.

(Real)

m7 Material parameter 7.

(Real)

Fsmooth Smooth strain rate flag.
=0
No strain rate smoothing.
= 1
Strain rate smoothing active.

(Integer)

Fcut Cutoff frequency for strain rate filtering.

(Real)

$\left[\frac{\text{1}}{\text{s}}\right]$
${\epsilon }_{0}$ Reference strain.

(Real)

Pmin Pressure cutoff (< 0).

Default = 1030 (Real)

$\left[\text{Pa}\right]$
$\rho {C}_{p}$ Specific heat per unit volume.

(Real)

$\left[\frac{\text{J}}{{\text{m}}^{3}\cdot \text{K}}\right]$
T0 Initial temperature.

(Real)

$\left[\text{K}\right]$
$\eta$ Heat conversion parameter 0 < $\eta$ < 1.0.

(Real)

## Example

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW103/1/1
Magnesium alloy
#        Init. dens.          Ref. dens.
0.0018              0.0018
#                  E                  Nu
45000                0.28
#                 A0                  M1                  M2                  M3                  M4
709.4             -0.0065             -0.1538                   0             -0.0261
#                 M5                  M7
0                   0
#            Fsmooth                Fcut                 Eps                Pmin
0                   0               0.010                   0
#              RhoCp                  T0                 ETA
1.89              673.15                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

1. Yield stress: 1(1)
${\sigma }_{y}={A}_{0}{\mathrm{exp}}^{{m}_{1}T}{\epsilon }^{{m}_{2}}{\stackrel{˙}{\epsilon }}^{{m}_{3}}{\mathrm{exp}}^{\frac{{m}_{4}}{\epsilon }}{\left(1+\epsilon \right)}^{{m}_{5}T}{\mathrm{exp}}^{{m}_{7}\epsilon }$
Where,
$T$
Temperature in °C
$\epsilon$
True strain $\epsilon ={\epsilon }_{0}+{\overline{\epsilon }}_{p}$
${\overline{\epsilon }}_{p}$
Equivalent plastic strain
$\stackrel{˙}{\epsilon }$
True strain rate in s-1
${m}_{1}$ - ${m}_{5}$
Material parameters
2. In case of purely mechanical simulation, the temperature is computed assuming adiabatic condition:(2)
$T={T}_{0}+\frac{\eta \cdot {E}_{\mathrm{int}}}{\rho {C}_{p}V}$
Where,
Eint
Internal energy of the element.
$\eta$
Taylor-Quinney coefficient used as scale of plastic energy, which transfers into heat.
$V$
Volume of the element
3. There is no strain rate effect if m3 = 0.
4. By default, the hydrostatic pressure is linearly proportional to volumetric strain:(3)
$P=K\mu$
Where,
$K=\frac{E}{3\left(1-2v\right)}$
Bulk modulus
$\mu =\frac{\rho }{{\rho }_{0}}-1$
Volumetric strain

An additional Equation of State (/EOS) card can refer to this material to model a nonlinear dependency between hydrostatic pressure and volumetric strain.

5. This material can be used with the material options, /HEAT/MAT, /THERM_STRESS/MAT, /EOS, and /VISC.
1 A. Hensel, T. Spittel, VEB German Pushling House for Basic Industry, Leipzig, Deutschland, 1978