A remeshing strategy for large deformations in the finite cell method

• Published in: Computers & mathematics with applications (1987) Vol. 80; no. 11; pp. 2379 - 2398
• Main Authors: Garhuom, Wadhah, Hubrich, Simeon, Radtke, Lars, Düster, Alexander
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.12.2020; Elsevier BV
• Subjects: Basis function removal; Cartesian coordinates; Deformation; Distortion; Finite cell method; Finite element method; Hyperelasticity; Large deformations; Radial basis function; Remeshing; Robustness; Stiffness; Radial basis function; Finite cell method; Remeshing; Basis function removal; Large deformations; Hyperelasticity
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2020.03.020

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.