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### Twenty-node brick element (C3D20)

This is a general purpose quadratic brick element (3x3x3 integration points). The shape functions can be found in [11]. The node numbering follows the convention of Figure 11 and the integration scheme is given in Figure 12.

Figure 11: 20-node brick element

Figure 12: 3x3x3 integration point scheme in hexahedral elements

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. [27].

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