A UNIFORM DEFORMATION GRADIENT HEXAHEDRON ELEMENT WITH ARTIFICIAL HOURGLASS CONTROL

An 8-noded linear hexahedron element for large strain hyperelastic analysis is presented in this paper. The element is based on a constant deformation gradient interpolation and is formulated using a mixed variational principle of the Hu-Washizu type. Volumetric and isochoric components of the deformation are treated independently to ensure the correct evaluation of the element volume. A simple procedure to control the propagation of spurious hourglass deformation modes is also discussed. This is based on the addition of artificial hourglass forces which vanish under constant deformation gradient conditions, thereby ensuring that the element passes a non-linear version of the patch test. Applications in the field of neo-Hookean materials and superplastic forming processes are also considered.