Mean-strain eight-node hexahedron with stabilization by energy sampling

A method for stabilizing the mean-strain hexahedron is described that differs from the currently known approaches. For simplicity, the developments are limited to linear elasticity but with an arbitrarily anisotropic elasticity matrix. The technique relies on a sampling of the stabilization energy using two quadrature rules, the mean-strain quadrature and the full Gaussian integration rule. The use of two quadrature rules is shown to guarantee consistency and stability. The stabilization energy is assumed to be generated by a modified constitutive matrix based on the spectral decomposition. The spectral decomposition of the constitutive matrix identifies the stiff and flexible modes of deformation. The stiff modes of deformation are only sampled by the mean-strain integration, which eliminates volumetric locking for isotropic materials as well as locking due to strongly anisotropic material properties. The accuracy and convergence characteristics of the present formulations compare favorably with the capabilities of mean-strain and other high-performance hexahedral elements as implemented in ABAQUS. Copyright (C) 2014 John Wiley & Sons, Ltd.