# 8.12. Examples

This section has several example problems. The geometric configuration for each problem is presented together with a brief description and the appropriate command lines.

## 8.12.1. Example 1

The first example problem has two blocks that come into contact due to initial velocity conditions. Block 1 has an initial velocity equal to \(v1\), and block 2 has an initial velocity equal to \(v2\). The geometric configuration for this problem is shown in Fig. 8.23.

Fig. 8.23 Problem with two blocks coming into contact.

The simplest input for this problem will be named `EXAMPLE1` and is shown as follows:

    BEGIN CONTACT DEFINITION EXAMPLE1
      #
      # define contact surfaces
      SKIN ALL BLOCKS = ON

      # set interactions
      BEGIN INTERACTION DEFAULTS
        GENERAL CONTACT = ON
      END

    END

In this example, the `SKIN ALL BLOCKS` command line with parameter set to `ON` will create a surface named `block_1` from the exterior skin of `block_1` and a surface named `block_2` from the exterior skin of `block_2`. The `GENERAL CONTACT = ON` command defines that `block_1` can contact `block_2`. As no friction model was specified, the default frictionless model is used for this interaction.

Now consider the same problem (two blocks coming into contact) in which it is desired that the two blocks interact with a coulomb friction model. The input for this variation of the two block problem will be named `EXAMPLE1A` and is shown as follows:

    BEGIN CONTACT DEFINITION EXAMPLE1A
      #
      # define contact surfaces
      SKIN ALL BLOCKS = ON

      # friction model definition
      BEGIN CONSTANT FRICTION MODEL rough
        FRICTION COEFFICIENT = 0.5
      END

      # set interactions
      BEGIN INTERACTION EX1A
        SURFACES = block_1 block_2
        FRICTION MODEL = rough
      END
    END

As was the case for the `EXAMPLE1` command block, the `SKIN ALL BLOCKS` command line with its parameter set to `ON` will create a surface named `block_1` from the skin of `block_1` and a surface named `block_2` from the skinning of `block_2`.

In order to have frictional contact between the two blocks, a constant Coulomb friction model is specified with a `CONSTANT FRICTION MODEL` command block. We name this model `ROUGH` and specify the coefficient of friction as `0.5`.

In the `INTERACTION` command block, the friction model `ROUGH` is selected on the `FRICTION MODEL` command line. This model is then applied to the interaction of surfaces `block_1` and `block_2`.

## 8.12.2. Example 2

A second more complex example problem has three blocks that come into contact due to initial velocity conditions. Block 1 is a solid element brick block with initial velocity equal to \(v1\). Block 3 is a solid element brick block with initial velocity \(v3\). Block 2 is a shell element block that has zero initial velocity. There is a side set (Surface 3) on the top faces of block 3. The geometric configuration for this problem is shown in Fig. 8.24.

Fig. 8.24 Problem with three blocks coming into contact.

The contact input for this three-block problem is called `EXAMPLE2` and is shown as follows:

    BEGIN CONTACT DEFINITION EXAMPLE2
      #
      # define contact surfaces
      CONTACT SURFACE b1 CONTAINS block_1
      CONTACT SURFACE b2 CONTAINS block_2
      CONTACT SURFACE s3 CONTAINS surface_3

      BEGIN CONSTANT FRICTION MODEL rough
        FRICTION COEFFICIENT = 0.5
      END
      #
      # set interactions
      BEGIN INTERACTION DEFAULTS
        FRICTION MODEL = rough
        GENERAL CONTACT = ON
        SELF CONTACT = ON
      END

      # set specific interaction
      BEGIN INTERACTION
        SURFACES = b2 s3
        FRICTION MODEL = FRICTIONLESS
      END

    END

In the `EXAMPLE2` command block, three surfaces have been defined. The first surface, `b1`, is obtained by skinning `block_1`. The second surface, `b2` is obtained by skinning `block_2`. The third surface, `s3`, is the user-defined side set `surface_3`.

In the `INTERACTION DEFAULTS` command block, we select the friction model `ROUGH` on the `FRICTION MODEL` command line. Both `GENERAL CONTACT` and `SELF CONTACT` are set to `ON`. For this problem the hollow cylinder, `block_2`, will undergo self-contact. Setting `GENERAL CONTACT` to `ON` will enforce contact between `b1` and `b2`, `b2` and `s3`, and `b1` and `s3`. Setting `SELF CONTACT` to `ON` will enable self-contact for all three of the surfaces.

For this particular example, we want to override some of the default setting for surface interactions which were previously set by the `INTERACTION DEFAULTS` command block. The `INTERACTION` command block shown in `EXAMPLE2` overrides these defaults and instead specifies surfaces `b2` and `s3` to have a frictionless interaction.

In Fig. 8.25, the bodies are shown after deformation and contact. The second image shows a cross section cut through the center. Due to the lofting of the shell surface there is a small gap between the shell elements themselves and the compressing blocks, which is expected. The actual contact geometry is shown in Fig. 8.26. Note that as `block_1` is skinned, the entire exterior surface of `block_1` is included in contact surface `b1`. The lofted geometry of the shell blocks is seen in this figure, this lofted geometry is both contacting with the blocks and experiencing self contact. Contact surface `s3` contains only the top sideset on `block_3`, not the entire skin.

Fig. 8.25 State of bodies after contact and deformation.

Fig. 8.26 Deformed contact geometry.