Finite element simulation of contact problems has become an indispensable tool in engineering analysis [1]. Contact constraints are typically enforced using Lagrange multipliers, penalty methods, or a combination of both approaches [2]. This thesis shall investigate a novel third medium contact formulation based on a space-filling mesh that enables contacting bodies to move and interact [3]. To accommodate contact constraints, the properties of the third medium embedding the bodies must adapt to their movements. The proposed approach employs an isotropic/anisotropic hyperelastic material model to represent the mechanical behaviour of the third medium. This eliminates the need for computationally expensive contact search algorithms and significantly simplifies the contact formulation. Preliminary results presented in [3] and independently computed using the high-order FEM code AdhoC [5] are encouraging (see Figure 1). The objective of this work is to study the third medium approach. The high-order finite element solver AdhoC will be employed to conduct comprehensive studies. These studies will assess the impact of the hyperelastic material model [1,3,4] on the convergence and stability of the contact algorithm, as well as the accuracy of the finite element solution in capturing the mechanical behavior of the system under contact conditions. The scope of the project will be tailored to the type of work (project or master thesis).
Recommended skills: Basic programming skills, finite elements
Literature
[1] P. Wriggers, Nonlinear Finite Methods, Springer, https://link.springer.com/book/10.1007/978-3-540-71001-1,2008.
[2] P. Wriggers, Computational Contact Mechanics, Springer, https://link.springer.com/book/10.1007/978-3-540-32609-0, 2006.
[3] P. Wriggers, J. Schröder, A. Schwarz, A finite element method for contact using a third medium, Computational Mechanics, 52:837-847, https://link.springer.com/article/10.1007/s00466-013-0848-5, 2013.
[4] J. Bonet, R.D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, https://doi.org/10.1017/CBO9780511755446, 2008.
[5] A. Düster, High-Order FEM, Lecture Notes, TU Hamburg, 2023.
[6] A. Düster, Nonlinear Structural Analysis, Lecture Notes, TU Hamburg, 2023.
Contact
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