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    A remeshing approach for the finite cell method applied to problems with large deformations
    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.
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    Extension of fictitious domain methods for vibroacoustic problems – Analysis of heterogeneous, foamed damping materials
    Even today, the prediction of the acoustical behaviour of components made of materials exhibiting a highly heterogeneous microstructure isa very demanding and challenging task. There are several reasons that make this problem so difficult to solve. On the one hand, the microstructure can only be accurately resolved if a large number of inite elements are deployed. On the other hand, all physically relevant interactions between the structural and fluid domain need to be taken into account. As mentioned before the body-fitted discretization of highly complex structures demands a large number of finite elements (degrees of freedom) and thus results in inacceptable computational times. Consequently, alternative methods, such as fictitious domain approaches, are required. Over the last years fictitious domain methods, such as the finite cell method (FCM), have proven their capabilities. To account for the vibroacoustic properties of microstructured materials these methods need to be extended. Therefore, the acoustic wave equation in the time domain or the Helmholtz equation in the frequency domain need to discretized by means of the FCM. Moreover, suitable coupling strategies that result in a weak or strong coupling need to be devised. Here, the main advantage of fictitious domain methods is the ability to take complex geometrical features into account while being able to straightforwardly superimpose cells with mechanical and fluidic properties. Thus, an efficient and robust strategy for vibroacoustic problems can be set up. Despite the application of nonconforming discretizations the numerical effort is still considerably large. Therefore, a second idea uses simplified numerical models based on homogenization techniques. To this end, the structure is assumed to consist of a homogeneous medium where the microstructure is neglected. In spite of this model simplification it is still expected to achieve reasonable results for specific applications. Besides the development of numerical methods a second focus is put on a comprehensive validation procedure. In this context, different experimental set-ups are deployed. To check the vibrational behavior of the structure under investigation a 3D laserscanning-vibrometer is used. In addition, the frequency-dependent acoustic parameters are measured by means of simple experimental set-ups such as an impedance tube and the results are compared to the numerically obtained values. As a last step the sound pressure radiation is tested in an anechoic room using microphone arrays and far field microphones. The acquired data are the foundation for illustrating the performance of the proposed methods.
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