# Solid isoparametric quadrilaterals and hexahedra

 The library of solid elements in Abaqus contains first- and second-order isoparametric elements. The following topics are discussed:
 Related Topics In Other Guides Solid (continuum) elements

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The first-order elements are the 4-node quadrilateral for plane and axisymmetric analysis and the 8-node brick for three-dimensional cases. The library of second-order isoparametric elements includes “serendipity” elements: the 8-node quadrilateral and the 20-node brick, and a “full Lagrange” element, the 27-node (variable number of nodes) brick. The term “serendipity” refers to the interpolation, which is based on corner and midside nodes only. In contrast, the full Lagrange interpolation uses product forms of the one-dimensional Lagrange polynomials to provide the two- or three-dimensional interpolation functions.

All these isoparametric elements are available with full or reduced integration. Gauss integration is almost always used with second-order isoparametric elements because it is efficient and the Gauss points corresponding to reduced integration are the Barlow points (Barlow, 1976) at which the strains are most accurately predicted if the elements are well-shaped.

The three-dimensional brick elements can also be used for the analysis of laminated composite solids. Several layers of different material, in different orientations, can be specified in each solid element. The material layers or lamina can be stacked in any of the three isoparametric coordinates, parallel to opposite faces of the master element (Figure 1). These elements use the same interpolation functions as the homogeneous elements, but the integration takes the variation of material properties in the stacking direction into account.

Hybrid pressure-displacement versions of these elements are provided for use with incompressible and nearly incompressible constitutive models (see Hybrid incompressible solid element formulation and Hyperelastic material behavior for a detailed discussion of the formulations used).