Single phase elements

The single phase solid elements (denoted by the extension solid) are general purpose elements implemented for simulating the response of a solid material. In addition, a set of porous elements (without solid) exists. These elements account for the porosity of a material on the element level, i.e. the density of the material is a function of void ratio and may change during the simulation due to compaction or expansion. The displacements of the solid are discretised at each node. For the practical application this means that:

• Solid elements interpret the assigned density as the density of the continuum (for the geotechnical engineer this means, that e.g. the dry density has to be prescribed). The density remains constant throughout the simulation.

• Porous elements on the other hand interpret the prescribed density as the density of the solid grains \(\rho^s\). The density of the continuum \(\rho\) is calculated based on the assigned porosity \(n\) (or void ratio) and \(\rho^s\):

  \[ \rho = (1-n) \cdot \rho^s \]

  It is obvious that although \(\rho^s\) remains constant during the simulation, \(\rho\) changes according to volume changes.

2D Elements

Element label	Dim.	Shape	Nodes	Order	nIP*	Remarks
u6 / u6-solid	2D	triangle	6	quadratic	3	(1)
u4 / u4-solid	2D	rectangle	4	linear	4	(1)
u4-solid-red	2D	rectangle	4	linear	1	(2)
u8 / u8-solid	2D	rectangle	8	quadratic	9	(1)

Axisymmetric Elements

Element label	Dim.	Shape	Nodes	Order	nIP*	Remarks
u4-ax / u4-solid-ax	axisym.	rectangle	4	linear	4	(1)
u6-ax / u6-solid-ax	axisym.	triangle	6	quadratic	3	(1)
u8-ax / u8-solid-ax	axisym.	rectangle	8	quadratic	9	(1)

3D Elements

Element label	Dim.	Shape	Nodes	Order	nIP*	Remarks
u8-3D / u8-solid-3D	3D	brick	8	linear	8	(1)
u8-solid-3D-red	3D	brick	8	linear	1	(2)
u20 / u20-solid	3D	brick	20	quadratic	27	(1), (3)
u20-red / u20-solid-red	3D	brick	20	quadratic	8	(3)
u27 / u27-solid	3D	brick	27	quadratic	27	(1)

Remarks

*	nIP = number of integration points
(1)	Due to the full integration, the element will behave badly for isochoric material behaviour. This shortcoming is more pronounced for linear interpolated elements and less pronounced for quadratic interpolated ones.
(2)	Reduced integration: This element does not suffer from the same locking issues as fully integrated elements, however, due to the rank deficiency of the element stiffness matrix, an Hourglass stiffness has to be applied to prevent spurious zero-energy modes. For more information see *Material and the Theory Manual
(3)	3D-serendipity elements such as the element are not suitable for contact analyses. The option bi-quadratic can be used to automatically transform u20 into u27 elements

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