Modified midpoint integration rule for the trilinear element in large deformation elasticity

In this paper we suggest two modified one-point Gauss integration rules for the Q1 bi- or trilinear element. The modifications both stabilize the hourglass modes of the one-point rule, and one of them is accurate also on severely distorted elements. We investigate the performance of the integration rules for the hexahedron element, and combine standard one-point integration of the volumetric terms with the modified rules for the isochoric terms to handle near incompressible situations.