Twenty-node brick element (C3D20)

The C3D20 element is a general purpose quadratic brick element (3x3x3 integration points). The shape functions can be found in [41]. The node numbering follows the convention of Figure 60 and the integration scheme is given in Figure 61.

**Figure 60:** 20-node brick element
$\begin{figure}\epsfig{file=C3D20.eps,width=10cm}\end{figure}$

**Figure 61:** 3x3x3 integration point scheme in hexahedral elements
$\begin{figure}\epsfig{file=Int27.eps,width=8cm}\end{figure}$

This is an excellent element for linear elastic calculations. Due to the location of the integration points, stress concentrations at the surface of a structure are well captured. However, for nonlinear calculations the elements exhibits the same disadvantages as the C3D8 element, albeit to a much lesser extent:

due to the full integration, the element will behave badly for isochoric material behavior, i.e. for high values of Poisson's coefficient or plastic behavior.
the element tends to be too stiff in bending, e.g. for slender beams or thin plates under bending. [98].