# C3D8

Linear Cube/Brick

* Number of Nodes: 8
* Number of DoFs: 3 (All Translation)
* DoF Label: U1, U2, U3
* Supports Body Force
* Constant Consistent Mass Matrix With Same Order Integration

## Syntax

```
element C3D8 (1) (2...9) (10) [11] [12] [13]
# (1) int, unique element tag
# (2...9) int, eight corner nodes with conventional order
# (10) int, material tag
# [11] string, integration scheme, default: "I"
# [12] bool string, nonlinear geometry switch, default: false
# [13] double, hourglassing penalty multiplier, default: 1.0
```

## Remarks

1. Three integration schemes are available, they are:
   1. "I" uses Irons six-point scheme.
   2. "R" uses reduced integration with Gauss scheme, that is one point at the center of the element. Hourglassing control is automatically enabled.
   3. "G" uses full integration (2nd order) with Gauss scheme.
2. The nonlinearity is implemented by using total Lagrangian (TL) formulation, turn on the switch to use it.

For the hourglassing control, see [10.1016/0045-7825(84)90067-7](https://doi.org/10.1016/0045-7825\(84\)90067-7). The hourglassing penalty multiplier (denoted as $$\mu$$) is an overall multiplier that is applied to the hourglassing stiffness matrix.

$$
\mu\mathbf{\gamma}\_i\mathbf{\gamma}\_i^\mathrm{T}.
$$

In the above, $$\mathbf{\gamma}\_i$$ is identical to Eq. (47) in the reference paper. Thus, $$\mu$$ shall be set to some value proportional to the elastic modulus.


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