# 2. Materials & Geometry

It is key to understand that materials are inputs into a model provided by the user. This article explains the material parameters required for a model and how to apply them to the grid or geometry.

## Material Properties

Material properties are another important aspect of the obtaining accurate simulation results. Material properties are inputs to the model and are not always easy to get hold from manufacturers. OnScale provides a database of materials to select from and is usually a great starting point for your simulation. However, the properties we have may differ to the actual materials you have used in your experiment so it is important to understand these differences and what impact they have on your results. For the most accurate simulation, you should characterise the materials you want to simulate.

The material types most commonly used in OnScale are:

1. Linear Elastic Isotropic (type elas)
• Material properties that are consistent in all axis directions
• Minimum required properties are density, bulk and shear moduli. Acoustic velocites can also be used instead of moduli
2. Anisotropic - Piezoelectric (type lean)
• Material properties are unique in each axis direction.
• Accurate modelling of piezoelectric materials requires the following parameters:
• Density
• 6 stiffness [c] or compliance [s] components
• 3 piezo electric stress [e] or strain [d] constants
• 2 dielectric constants [εS]
3. Nonlinear - Biological (type tisu)
• Nonlinear effects can be supported provided that pressure levels are high enough to initiate them.
• Additional material properties require additional inputs over conventional linear elastic materials:
• B/A - B over A (commonly know for biological materials)
• Maximum pressure cut-off - negative number as compression is negative in OnScale
• Minimum pressure cut-off - set to a large positive number for wave 'steepening'

Material damping must also be defined to accurately simulate your materials. OnScale offers a number of damping models to be used depending on your material type:

• Stiffness damping - sdmp command
• Mass damping - mdmp command
• Rayleigh damping - rdmp command
• Viscoelastic damping - vdmp command

The method of definition is similar across each of the damping models and requires the following information:

1. name of the material
2. frequency at which the damping model is centered at
3. damping option allows the convention of damping values to be set - Q-factor (q); dB/distance (db) or Fraction of critical damping (crit)
4. dilatational wave attenuation value
5. shear wave attenuation value
6. Frequency at which the attenuation values were measured at
7. exponent to control how damping varies with frequency
8. Only if option was set to db – sets the distance over which the damping values are achieved

### Designer Mode

OnScale provides an extensive material database to browse and select from using the Material Tool. This allows you to select/edit/create materials that you would like to use in your model. Any selected material will automatically appear in your model tree ready to be used:

### Analyst Mode

The matr command and its subset of commands are required to fully define a material:

Linear Elastic Material - using bulk and shear moduli:

`matr    type elas    wvsp off    prop epoxy \$density \$bulkmod \$shearmod`

Linear Elastic Material - using bulk and shear velocities:

`matr    type elas    wvsp on    prop epoxy \$density \$vellong \$velshear`

Anisotropic - Piezoelectric:

```matr    type lean    prop pmt3 \$rho    \$c11 \$c12 \$c13 0.0 0.0 0.0 \$c11    \$c13 0.0 0.0 0.0 \$c33 0.0 0.0    0.0 \$c44 0.0 0.0 \$c44 0.0 \$c66
piez pmt3 1 5 \$ex5 2 4 \$ex5 3 1 \$ez1 3 2 \$ez1 3 3 \$ez3    elec pmt3 \$epxx \$epxx \$epzz    axis pmt3 posy```

Non Linear Material - Biological tissue:

`matr    wvsp on    type tisu    symb pmax = 2.e6    symb pmaxn = -2.e6    symb ba = 10.0    prop fatnl 928. 1427. 0. 0.01 0.0 0.0    \$ba \$pmaxn \$pmax`

Damping definitions - viscoelastic damping using the db option

`vdmp epoxy \$freqdamp db \$attlong \$attenshear \$measuref \$exponent \$dist`

Damping definitions - Rayleigh damping using the q option

`rdmp piezo \$freqdamp q \$attlong \$attenshear \$measuref \$exponent `

`c allocate materials to gridsite regn watr /* assign watr to full grid regn pmt3 \$i1 \$i2 \$j2 \$j3 /* assign material 'pmt3' to grid defined by nodal rangeend`