Theory Manual Version 3.4
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Chapter 4: Element Library Up Chapter 4: Element Library Subsection 4.1.1: Hexahedral Elements

4.1 Solid Elements

The 3D solid elements available in FEBio are isoparametric elements. All of the solid elements are formulated in a global Cartesian coordinate system. For all these elements, a local coordinate system (so-called isoparametric coordinates) is defined as well. The global position vector can be written as a function of the isoparametric coordinates in the following sense: Here, is the number of nodes, , and are the isoparametric coordinates, are the element shape functions and are the spatial coordinates of the element nodes. The same parametric interpolation is used for the interpolation of other scalar and vector quantities.
All elements in FEBio are integrated numerically. This implies that integrals over the volume of the element are approximated by a sum: Here, is the biunit cube, is the number of integration points, are the location of the integration points in isoparametric coordinates, is the Jacobian of the transformation , and is a weight associated with the integration point. The integration is performed over the element's volume in the natural coordinate system.
Most fully integrated solid elements are unsuitable for the analysis of (nearly-) incompressible material behavior. To deal with this type of deformation, a three-field element implementation is available in FEBio [67].
Chapter 4: Element Library Up Chapter 4: Element Library Subsection 4.1.1: Hexahedral Elements