A remeshing strategy for large deformations in the finite cell method

Journal
Computers and mathematics with applications  
Volume
80
Issue
11
Start Page
2379
End Page
2398
Citation
Computers and Mathematics with Applications 11 (80): 2379-2398 (2020)
Publisher DOI
10.1016/j.camwa.2020.03.020
Scopus ID
2-s2.0-85083051928
Publisher
Elsevier Science
The simulation of large structural deformations with the finite element method poses several challenges. The severe distortion of elements may deteriorate the accuracy and robustness of the method and restrict it to smaller deformations than desired. This issue is especially present in the finite cell method (FCM), where complex geometries are discretized with a non-conforming Cartesian grid introducing a fictitious material with very low stiffness. The remeshing strategy presented here improves the robustness at the cost of generating a new Cartesian grid of the deformed geometry at load steps where the element distortion becomes critical. This allows us to use larger load steps and to further deform the structure under consideration. We use radial basis functions to transfer the displacements and the displacement gradients from one mesh to the next one. The method is investigated in combination with a hyperelastic material and exemplary applied to simulate a pore of a foam.
Subjects
Basis function removal
Finite cell method
Hyperelasticity
Large deformations
Radial basis function
Remeshing
DDC Class
600: Technik
Funding(s)
SPP 1748: Teilprojekt "High-Order Immersed-Boundary-Methoden in der Festkörpermechanik für generativ gefertigte Strukturen"  
More Funding Information
The authors gratefully acknowledge support by the Deutsche Forschungsgemeinschaft, Germany in the Priority Program 1748 “Reliable simulation techniques in solid mechanics. Development of non-standard discretization methods, mechanical and mathematical analysis” under the project DU 405/8-2 .