A virtual element method for contact modeling and dynamics

authored by: Mertcan Cihan
supervised by: Peter Wriggers
Abstract: Decreasing resources and limited energy results in a greater demand for virtual development processes and efficient product development. This trend points out the importance of digitalization and the subsequent need for efficient and accurate numerical prediction methods for product development. Due to their flexibility, numerical methods are gradually and steadily replacing physical tests in industrial product developments. The finite element method is perhaps the most well-known and widely used numerical method in industry and science. Increasing computer capabilities and further developments of these methods in recent years have increased the amount of application fields, including civil, automotive, naval, space and geo-technical engineering. However, along with complex geometries the spatial discretization of the domain emerges as a very time consuming step. Due to the fact that the classical finite element method is restricted to basic regular shaped element topologies, a more general choice of element shapes would give more flexibility. Within mesh-based methods, polygonal methods are a helpful alternative and showed great performance in engineering and science. However, most of these methods seem to need more computational effort and beside the aforementioned advantage of flexible element shapes, disadvantages appear as well. A relatively new method, the virtual element method, promises great numerical properties and can be seen as a generalization of the classical finite element method. All new methods need to be investigated for different applications in engineering and science before they can be applied commercially. This work deals with the application of the virtual element method to dynamic and elastoplastic material behavior. To deal with elastic and plastic incompressibility, a mixed virtual element formulation is presented as well. As a further development, the virtual element method is used to model three dimensional contact with different contact discretizations. A new projection algorithm is developed to manipulate the mesh at the contact interface, such that a very simple and efficient node-to-node contact formulation can be used. Various numerical examples for all aforementioned applications are performed, including benchmark problems such as the classical patch test. For comparison purposes, different finite element formulations are also adopted. As a final example, all models, including plasticity, dynamics and contact, are coupled to model mechanical impact.
Organisation(s): Institute of Continuum Mechanics
Type: Doctoral thesis
No. of pages: 136
Publication date: 2023
Publication status: Published
Electronic version(s): https://doi.org/10.15488/14600 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@phdthesis{b8397d0057e44286b23bcf5b75d69cda,
title = "A virtual element method for contact modeling and dynamics",
abstract = "Decreasing resources and limited energy results in a greater demand for virtual development processes and efficient product development. This trend points out the importance of digitalization and the subsequent need for efficient and accurate numerical prediction methods for product development. Due to their flexibility, numerical methods are gradually and steadily replacing physical tests in industrial product developments. The finite element method is perhaps the most well-known and widely used numerical method in industry and science. Increasing computer capabilities and further developments of these methods in recent years have increased the amount of application fields, including civil, automotive, naval, space and geo-technical engineering. However, along with complex geometries the spatial discretization of the domain emerges as a very time consuming step. Due to the fact that the classical finite element method is restricted to basic regular shaped element topologies, a more general choice of element shapes would give more flexibility. Within mesh-based methods, polygonal methods are a helpful alternative and showed great performance in engineering and science. However, most of these methods seem to need more computational effort and beside the aforementioned advantage of flexible element shapes, disadvantages appear as well. A relatively new method, the virtual element method, promises great numerical properties and can be seen as a generalization of the classical finite element method. All new methods need to be investigated for different applications in engineering and science before they can be applied commercially. This work deals with the application of the virtual element method to dynamic and elastoplastic material behavior. To deal with elastic and plastic incompressibility, a mixed virtual element formulation is presented as well. As a further development, the virtual element method is used to model three dimensional contact with different contact discretizations. A new projection algorithm is developed to manipulate the mesh at the contact interface, such that a very simple and efficient node-to-node contact formulation can be used. Various numerical examples for all aforementioned applications are performed, including benchmark problems such as the classical patch test. For comparison purposes, different finite element formulations are also adopted. As a final example, all models, including plasticity, dynamics and contact, are coupled to model mechanical impact.",
author = "Mertcan Cihan",
year = "2023",
doi = "10.15488/14600",
language = "English",
isbn = " 978-3-941302-51-8",
publisher = "Institut f{\"u}r Kontinuumsmechanik, Leibniz Universit{\"a}t Hannover",
school = "Leibniz University Hannover",
}