Summary: The optimization of finite element discretizations within energy-momentum time integrations of thermodynamical problems leads to further ‘constraints’ on algorithmic modifications compared to static problems, because each modification must not violate discrete balance laws. In order to preserve each discrete balance law while modifying the space approximation, a mixed version of the principle of virtual power is applied. Besides the reduction of volumetric locking in the matrix material and line locking in the fibers of the considered transversely isotropic continuum, a new space approximation additionally prevents spurious shear deformations in bending dominated problems. This approximation is based on independent fields for the deformation gradient and the first Piola-Kirchhoff stress tensor, leading to a new B-bar operator. The local shape functions for the independent deformation gradient are derived by a new criterion from the finite element shape functions. In this way, linear and quadratic hexahedral finite elements are combined with standard and non-standard shape functions of tetrahedral and prismatic elements. In order to evaluate the performance of this new mixed B-bar method with respect to locking as well as thermodynamical behavior, numerical examples with thin-walled, fiber-reinforced structures are considered. The numerical examples also reveal a new aspect of structure preservation, namely, the goal of a spatial mesh density independent structure preservation.