Low-Density Foam

Uniaxial Tension and Compression Data

Uniaxial stress strain data are in terms of nominal stresses (force per unit of original cross-section area) and nominal strains (change in length per unit of original length). Poisson effects are modeled by specifying lateral strains. For explicit time integration, rate dependence is modeled by specifying stress strain data at different strain rates. Three strain rate measures are available when Poisson effects are neglected: volumetric strain rate; strain rate along each principal direction to evaluate principal stress in that direction; and a maximum of principal direction strain rates to evaluate stress-strain response along each principal direction. However, when Poisson effects are included, only the maximum of principal direction rates is available as the strain measure to compute stress-strain response along each principal direction. The stress-strain curves at different strain rates should not intersect because it would produce an unstable material. For implicit integration, the material response is based on quasi-static behavior and strain rate dependence is not needed.

Table 1. Options for specifying uniaxial test data

Label	Description
Lateral strain data	Select Yes to specify lateral nominal lateral strain for modeling Poisson effect; select No otherwise.
Strain rate	Strain rate measure used for stress-strain response.
Enable rate extrapolation	Extrapolates strain rate dependent stress-strain data beyond maximum specified strain rate.

Table 2. Uniaxial compression or tension table column data

Label	Description
Nominal stress	Nominal stress values. Specify absolute values for compression so that they are positive.
Nominal strain	Nominal strain values. Specify absolute values for compression so that they are positive.
Nominal lateral strain	Positive nominal lateral strain values when specifying compression data and negative values for tension data to model Poisson effects.
Use strain-rate dependent data	Specify stress-strain data as a function of strain rates
Use temperature-dependent data	Specifies temperature dependent stress-strain data. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies field variable dependent stress-strain data. A Field field appears in the data table each time the number of field variables is incremented by one. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Additional Low Density Foam data

The following additional data is only relevant when explicit time integration is used. For implicit time integration, the data is ignored.

Table 3. Low Density Foam tensile failure data

Label	Description
Specify tension cutoff	Specifies maximum principal stress the low-density material can sustain in tension.
Enable failure	Enables element deletion when tension cutoff is specified and the value reached; Force maximum principal stress to be below the tension cutoff value otherwise.

Sudden changes in deformation rates can cause stress jumps. They can be prevented using viscous regularization with relaxation time given by:

Here, ${\mu }_0$ and ${\mu }_1$ are linear and non-linear viscocity parameters while exponent $\alpha$ models the non-linearity as a function of material stretch $\lambda$ .

Table 4. Relaxation coefficients data

Parameter	Description
mu0	Linear viscocity parameter, ${\mu }_0$ .
mu1	Non-linear viscocity parameter, ${\mu }_1$ .
alpha	Sensitivity parameter, $\alpha$ .