Mean-strain 8-node hexahedron with optimized energy-sampling stabilization

A method for stabilizing the mean-strain hexahedron was described by Krysl (in IJNME 2014). The technique relied on a sampling of the stabilization energy using the mean-strain quadrature and the full Gaussian integration rule, which was shown to guarantee consistency and stability. The stabilization energy was assumed to be generated by a modified constitutive matrix based on the spectral decomposition. The stabilization required user-selected values of the stabilization parameters. In the present work we eliminate the arbitrariness of the stabilization parameters. We formulate the technique more precisely as an assumed-strain method, and we express the stabilization energy in terms of input parameters of the real material. Finally, we fix the value of the stabilization parameters in a quasi-optimal manner by linking the stabilization to the bending behavior of the hexahedral element. For simplicity the developments are limited to linear elasticity, but with an arbitrarily anisotropic elasticity matrix. 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 and with a number of successful hexahedral and shell elements and we demonstrate that the present element performs very well when used with large aspect ratios for thin structures such as plates or shells.