The 8-node hexahedron (or brick element) is a 6-sided solid element with linear shape functions formulated as an isoparametric element. To get accurate results using this element, the mesh needs to be relatively small. It is recommended that there are at least six elements in any direction to achieve reasonable accuracy. If the mesh is coarser than this, consider using the 20-node hexahedron, which is a quadratic element and can achieve much better accuracy with significantly fewer elements (at the cost of computation time).

References

1. Abaqus Theory Manual - Isoparametric Continuum Elements
2. Nikishkov, G. P. "Introduction to the Finite Element Method." University of Aizu, Aizu-Wakamatsu 965-8580, Japan. 2007 Lecture Notes

Element Geometry

The 8-node hexahedron is formulated as an isoparametric element such that element geometry is inconsequential. The local isoparametric coordinate axes are $\xi,\eta,$ & $\gamma$. It contains eight vertex nodes, none of which have rotational degrees of freedom.

Where:

$-1≤\xi≤1$

$-1≤\eta≤1$

$-1≤\gamma≤1$

Degrees of Freedom

The 8-node hexahedron formulation contains three degrees-of-freedom (DoFs) at each node:

1. x-translation
2. y-translation
3. z-translation

There are 8 nodes defined for this formulation. These nodes are numbered from 1 to 8 in a counter-clockwise direction, bottom surface first, then top surface.

The local stiffness matrix is formulated with the following degree-of-freedom order:

$\begin{bmatrix}x_1 & y_1 & z_1 & x_2 & y_2 & z_2 & ..... & x_{15} & y_{15} & z_{15} \end{bmatrix}$

Where: