Novel Finite Elements

Mixed, Hybrid and Virtual Element Formulations at Finite Strains for 3D Applications

authored by: Jörg Schröder, Peter Wriggers, Alex Kraus, Nils Viebahn
Abstract: The main goal of this research project is to develop new finite-element formulations as a suitable basis for the stable calculation of modern isotropic and anisotropic materials with a complex nonlinear material behavior. New ideas are pursued in a strict variational framework, based either on a mixed or virtual FE approach. A novel extension of the classical Hellinger-Reissner formulation to non-linear applications is developed. Herein, the constitutive relation of the interpolated stresses and strains is determined with help of an iterative procedure. The extension of the promising virtual finite element method (VEM) is part of the further investigation. Particularly, different stabilization methods are investigated in detail, needed in the framework of complex nonlinear constitutive behavior. Furthermore the interpolation functions for the VEM is extended from linear to quadratic functions to obtain better convergence rates. Especially in this application the flexibility of the VEM regarding the mesh generation will constitute a huge benefit. As a common software development platform the AceGen environment is applied providing a flexible tool for the generation of efficient finite element code.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Duisburg-Essen
Type: Contribution to book/anthology
Pages: 37-67
No. of pages: 31
Publication date: 2022
Publication status: Published
ASJC Scopus subject areas: Mechanical Engineering, Computational Theory and Mathematics
Electronic version(s): https://doi.org/10.1007/978-3-030-92672-4_2 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@inbook{bd446c4622954f2599a340183b930a0a,
title = "Novel Finite Elements: Mixed, Hybrid and Virtual Element Formulations at Finite Strains for 3D Applications",
abstract = "The main goal of this research project is to develop new finite-element formulations as a suitable basis for the stable calculation of modern isotropic and anisotropic materials with a complex nonlinear material behavior. New ideas are pursued in a strict variational framework, based either on a mixed or virtual FE approach. A novel extension of the classical Hellinger-Reissner formulation to non-linear applications is developed. Herein, the constitutive relation of the interpolated stresses and strains is determined with help of an iterative procedure. The extension of the promising virtual finite element method (VEM) is part of the further investigation. Particularly, different stabilization methods are investigated in detail, needed in the framework of complex nonlinear constitutive behavior. Furthermore the interpolation functions for the VEM is extended from linear to quadratic functions to obtain better convergence rates. Especially in this application the flexibility of the VEM regarding the mesh generation will constitute a huge benefit. As a common software development platform the AceGen environment is applied providing a flexible tool for the generation of efficient finite element code.",
author = "J{\"o}rg Schr{\"o}der and Peter Wriggers and Alex Kraus and Nils Viebahn",
note = "Funding Information: Acknowledgements The authors gratefully acknowledge the support by the Deutsche Forschungs-gemeinschaft in the Priority Program 1748 “Reliable Simulation Techniques in Solid Mechanics, Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis” for the project “Novel finite elements for anisotropic media at finite strain” (Project number: 255432295, IDs: WR 19/50-1, SCHR 570/23-1).",
year = "2022",
doi = "10.1007/978-3-030-92672-4_2",
language = "English",
isbn = "978-3-030-92671-7",
series = "Lecture Notes in Applied and Computational Mechanics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "37--67",
editor = "J{\"o}rg Schr{\"o}der and Peter Wriggers",
booktitle = "Non-standard Discretisation Methods in Solid Mechanics",
address = "Germany",
}