An enhanced single Gaussian point continuum finite element formulation using automatic differentiation

Finite Elements in Analysis and Design, vol. 246, pp. 104329

Abstract

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 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 .

Authors 6

1. Njomza Pacolli corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Applied Mechanics, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

2. Jannick Kehls Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Applied Mechanics, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

3. Bjorn Sauren Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Chair of Structural Analysis and Dynamics, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

4. Sven Klinkel Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Chair of Structural Analysis and Dynamics, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

5. Stefanie Reese Aachen Institute of Applied Mechanics

   University of Siegen · RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Applied Mechanics, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

   University of Siegen, Adolf-Reichwein-Straße 2a, 57076 Siegen, Germany

6. Hagen Holthusen Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Applied Mechanics, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany