A remeshing approach for the finite cell method applied to problems with large deformations

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The primary goal of the proposed research project is to further develop the finite cell method (FCM) - a high-order fictitious domain approach - for large deformation analysis including finite strain problems of elastoplasticity. Foamed materials will be used as a demonstrator application, as they feature complex geometries and a complex deformation behavior. Recently, we introduced a remeshing strategy to improve the robustness of the FCM for large deformations. Here, the deformed structure is remeshed when finite cells are distorted too severely. Since the FCM applies Cartesian grids, the remeshing is simple and can be carried out fully automatically. The method performs well for hyperelastic finite strain problems, and the structure under consideration can be deformed much further when applying the remeshing strategy. Nevertheless, there are still many open questions which we would like to address in this project. First of all, different remeshing criteria need to be developed and investigated in order to reliably determine when remeshing has to be initiated during the analysis. Another considerable challenge in elastoplastic analysis – because of the non-smooth data – is the interpolation of history data from the old to the new mesh. Therefore, error-controlled interpolation algorithms need to be developed. Since the computation of the element/cell matrices accounts for a significant part of the overall effort in high-order methods, special attention will be placed on this point. This is of great importance since the finite cell method requires a dense set of integration points to resolve the geometry of the broken cells. In addition, the nonlinear material models with an increased numerical effort at each integration point, combined with the repeated computation of the tangent stiffness matrix will increase the numerical effort. Thus, we aim at reducing the number of integration points. This can be achieved by applying the moment fitting where a quadrature rule is derived for every broken cell. To this end, we will extend and study the moment fitting for the case of finite strain elastoplasticity. In order to judge the robustness, accuracy, and efficiency of the overall remeshing approach, we will consider carefully selected benchmark problems and compare the proposed method with other finite element formulations.