Details
| Original language | English |
|---|---|
| Title of host publication | Non-standard Discretisation Methods in Solid Mechanics |
| Editors | Jörg Schröder, Peter Wriggers |
| Publisher | Springer Science and Business Media Deutschland GmbH |
| Pages | 37-67 |
| Number of pages | 31 |
| ISBN (electronic) | 978-3-030-92672-4 |
| ISBN (print) | 978-3-030-92671-7 |
| Publication status | Published - 2022 |
Publication series
| Name | Lecture Notes in Applied and Computational Mechanics |
|---|---|
| Volume | 98 |
| ISSN (Print) | 1613-7736 |
| ISSN (electronic) | 1860-0816 |
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.
ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
Cite this
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Non-standard Discretisation Methods in Solid Mechanics. ed. / Jörg Schröder; Peter Wriggers. Springer Science and Business Media Deutschland GmbH, 2022. p. 37-67 (Lecture Notes in Applied and Computational Mechanics; Vol. 98).
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research
}
TY - CHAP
T1 - Novel Finite Elements
T2 - Mixed, Hybrid and Virtual Element Formulations at Finite Strains for 3D Applications
AU - Schröder, Jörg
AU - Wriggers, Peter
AU - Kraus, Alex
AU - Viebahn, Nils
N1 - 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).
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85128602916&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-92672-4_2
DO - 10.1007/978-3-030-92672-4_2
M3 - Contribution to book/anthology
AN - SCOPUS:85128602916
SN - 978-3-030-92671-7
T3 - Lecture Notes in Applied and Computational Mechanics
SP - 37
EP - 67
BT - Non-standard Discretisation Methods in Solid Mechanics
A2 - Schröder, Jörg
A2 - Wriggers, Peter
PB - Springer Science and Business Media Deutschland GmbH
ER -