This contribution presents an improved low-order 3D finite element formulation with hourglass stabilization using automatic differentiation (AD). Here, the former Q1STc formulation is enhanced by an approximation-free computation of the inverse Jacobian. To this end, AD tools automate the computation and allow a direct evaluation of the inverse Jacobian, bypassing the need for a Taylor series expansion. Thus, the enhanced version, Q1STc+, is introduced. Numerical examples are conducted to compare the performance of both element formulations for finite strain applications, with particular focus on distorted meshes. Moreover, the performance of the new element formulation for an elasto-plastic material is investigated. To validate the obtained results, a volumetric locking-free reference element based on scaled boundary parametrization is used. Both the implementation of the element routine Q1STc+ and the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.14259791

翻译：本文提出了一种采用自动微分（AD）技术并具有沙漏稳定性的改进型低阶三维有限元公式。在此，原有的Q1STc公式通过无近似的逆雅可比矩阵计算得到增强。为此，自动微分工具自动化了计算过程，并允许直接求值逆雅可比矩阵，从而绕过了泰勒级数展开的需求。因此，增强版本Q1STc+被引入。通过数值算例比较了两种单元公式在有限应变应用中的性能，特别关注了扭曲网格的情况。此外，还研究了新单元公式在弹塑性材料中的性能。为验证所得结果，采用了基于比例边界参数化的无体积闭锁参考单元。单元程序Q1STc+及其相应材料子程序的实现已在https://doi.org/10.5281/zenodo.14259791公开提供。