/MAT/LAW88
Block Format Keyword This law represents the behavior of a hyperelastic material with strain rate effects. This law is generally used to model incompressible rubbers, polymers, foams, and elastomers. It is defined by a family of stress versus strain curves at different strain rates.
Unloading can be represented using an unloading function or by providing hysteresis and shape factor inputs to a damage model based on energy. This law is only compatible with solid elements.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW88/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
$\nu $  K  F_{cut}  F_{smooth}  N_{L}  
fct_ID_{unL}  Fscale_{unL}  Hys  Shape  Tension 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{Li}  Fscale_{Li}  ${\dot{\epsilon}}_{Li}$ 
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) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
$\nu $  Poisson ratio. For incompressible materials 0.495 is maximum value. Default = 0.495 (Real) 

K  Bulk modulus. (Real) 
$\left[\text{Pa}\right]$ 
F_{cut}  Cutoff frequency for strain rate
filtering. Default = 10^{30} (Real) 
$\text{[Hz]}$ 
F_{smooth}  Smooth strain rate option flag.
(Integer) 

N_{L}  Number of loading stress strain
curve. (Integer) 

fct_{unL}  Unloading engineering stress versus
engineering strain function identifier. 3 (Integer) 

Fscale_{unL}  Unloading function scale
factor. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Hys  Hysteresis unloading factor. Ignore if,
unloading function is used. 3 0.0 ≤ Hys ≤ 1.0 Default = 0.0 (Real) 

Shape  Shape factor. Ignored if, unloading
function is used. 3 Default = 1.0 (Real) 

Tension  Unloading rate effects option
flag. During loading in tension or compression, the loading strain rate
dependent curves are always used. For unloading, the following options are available:


fct_ID_{Li}  Loading function identifier defining
engineering stress versus engineering strain for i^{th} strain rate
function. (Integer) 

${\dot{\epsilon}}_{Li}$  Strain rate for i^{th} loading
engineering stress versus engineering strain function. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Fscale_{Li}  Scale factor for i^{th} loading
function. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Example (Rubber)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
kg mm ms
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW88/1/1
rubber
# RHO_I
1E6
# NU K F_cut F_smooth N_L
.495 19.93 0 1
#fctID_Unl Fscale_unload HYs Shape Tension
1 1. 0. 0. 0
#fctID_l Fscale_load Eps_._load
1 1. 0.
#12345678910
/FUNCT/1
function 1
# X Y
8.51E01 3.55E+01
7.76E01 1.10E+01
7.02E01 4.83E+00
6.01E01 2.06E+00
5.00E01 1.05E+00
4.05E01 5.98E01
3.04E01 3.33E01
0.00E+00 0.00E+00
4.05E01 1.53E01
8.50E01 2.37E01
#12345678910
#ENDDATA
#12345678910
Comments
 This model utilizes an Ogden material formulation. Material parameters are directly derived from the input stress strain curves from uniaxial tests for different strain rates. The material is assumed to be nearly incompressible with Poisson’s ratio = 0.495.
 Strain rate effects can be modeled by
including loading engineering stress strain test data at different strain rates
fct_ID_{Li}. This can be easier than
calculating viscous parameters for traditional hyperelastic material models. When using
stress strain curves at different strain rates, the following suggestions are
recommended:
 The stress strain curve should be monotonic increasing and smooth. The derivattive of the stress strain curve should be smooth.
 Enable strain rate smoothing by defining, F_{smooth} =1 with F_{cut} =500 Hz.
 In /PROP/SOLID define I_{HKT} =2 and if needed, increase the Numerical Navier Stokes viscosity.
 Unloading can be represented using an
unloading function, Fscale_{unL}, or by
providing hysteresis, Hys, and
shape factor, Shape,
inputs to a damage model based on energy.When using the damage model, the loading curves are used for both loading and unloading and the unloading stress tensor is reduced by:
(1) $$\sigma =\left(1D\right)\sigma $$with(2) $$D=\left(1Hys\right)\left(1{\left(\frac{{W}_{cur}}{{W}_{\mathrm{max}}}\right)}^{Shape}\right)$$Where, ${W}_{cur}$
 Current energy
 ${W}_{\mathrm{max}}$
 Maximum energy corresponding to the quasistatic behavior
If the unloading function, Fscale_{unL}, is entered, unloading is defined based on the unloading flag, Tension.
 /VISC/PRONY can be used with this material law to include viscous effects.