TY - CHAP A1 - Bauer, Monika A1 - Gwiazda, Maciej A1 - Müller, Ralf A1 - Decker, Daniel T1 - RTM-Materials Based on Silazane-Resin-Systems T2 - Proceedings, 7th International Conference on High Temperature Ceramic Matrix Composites (HT-CMC 7), September 20 - 22, 2010 in Bayreuth KW - new generation of RTM-resins KW - RTM KW - hybrid resins Y1 - 2010 PB - AVISO Verl.-Ges. CY - Berlin ER - TY - GEN A1 - Stohwasser, Ralf A1 - Giesebrecht, Jan A1 - Kraft, Regine A1 - Müller, Eva-Christiane A1 - Häusler, Karl Georg A1 - Kettenmann, Helmut A1 - Hanisch, Uwe-Karsten A1 - Kloetzel, Peter-Michael T1 - Biochemical analysis of proteasomes from mouse microglia: induction of immunoproteasomes by interferon-gamma and lipopolysaccaride T2 - Glia Y1 - 2000 U6 - https://doi.org/10.1002/(SICI)1098-1136(20000215)29:4<355::AID-GLIA6>3.0.CO;2-4 SN - 1098-1136 SN - 0894-1491 VL - 29 IS - 4 SP - 355 EP - 365 ER - TY - GEN A1 - Heuberger, Maria A1 - Grill, Eva A1 - Saglam, Murat A1 - Ramaioli, Cecilia A1 - Müller, Martin A1 - Strobl, Ralf A1 - Holle, Rolf A1 - Peters, Annette A1 - Schneider, Erich A1 - Lehnen, Nadine T1 - Usability of the Video Head Impulse Test: Lessons from the Population-Based Prospective KORA Study T2 - Frontiers in Neurology Y1 - 2018 U6 - https://doi.org/10.3389/fneur.2018.00659 SN - 1664-2295 VL - 9 ER - TY - GEN A1 - Schmidt, Simon A1 - Dornisch, Wolfgang A1 - Müller, Ralf T1 - A phase field model for martensitic transformation coupled with the heat equation T2 - GAMM‐Mitteilungen N2 - In order to consider temperature dependency in a phase field model for martensitic transformations a temperature dependent phase separation potential is introduced. The kinematics and the energetic setup underlying the phase transformation are briefly explained. Parameters are identified using molecular dynamics (MD) simulations. The kinetics of the phase field model are in good agreement with those of the MD simulations. Further, the effect of temperature on the microstructure evolution is studied for varying initial austenite contents. KW - Solidifcation KW - phase-field KW - theory of porous media KW - finite element method KW - multi-scale Y1 - 2017 U6 - https://doi.org/10.1002/gamm.201720005 SN - 1522-2608 VL - 40 IS - 2 SP - 138 EP - 153 ER - TY - GEN A1 - Dornisch, Wolfgang A1 - Schrade, David A1 - Xu, Bai-Xiang A1 - Keip, Marc-André A1 - Müller, Ralf T1 - Coupled phase field simulations of ferroelectric and ferromagnetic layers in multiferroic heterostructures T2 - Archive of Applied Mechanics N2 - The combination of materials with either pronounced ferroelectric or ferromagnetic effect characterizes multiferroic heterostructures, whereby the different materials can be arranged in layers, columns or inclusions. The magnetization can be controlled by the application of electrical fields through a purely mechanical coupling at the interfaces between the different materials. Thus, a magneto-electric coupling effect is obtained. Within a continuum mechanics formulation, a phase field is used to describe the polarization and the magnetization in the ferroelectric and ferromagnetic layers, respectively. The coupling between polarization/magnetization and strains within the layers, in combination with the mechanical coupling at the sharp layer interfaces, yields the magneto-electric coupling within the heterostructure. The continuum formulations for both layers are discretized in order to make the differential equations amenable to a numerical solution with the finite element method. A state-of-the-art approach is used for the ferroelectric layer. The material behavior of the ferromagnetic layer is described by a continuum formulation from the literature, which is discretized using a newly proposed approach for the consistent interpolation of the magnetization vector. Four numerical examples are presented which show the applicability of the newly proposed approach for the ferromagnetic layer as well as the possibility to simulate magneto-electric coupling in multiferroic heterostructures. KW - Multiferroic heterostructure KW - Phase field method KW - Ferroelectric material KW - Ferromagnetic material KW - Finite element method KW - Rotation interpolation Y1 - 2019 U6 - https://doi.org/10.1007/s00419-018-1480-9 SN - 0939-1533 SN - 1432-0681 VL - 89 IS - 6 SP - 1031 EP - 1056 ER - TY - GEN A1 - Nadgir, Omkar A1 - Dornisch, Wolfgang A1 - Müller, Ralf A1 - Keip, Marc-André T1 - A phase-field model for transversely isotropic ferroelectrics T2 - Archive of Applied Mechanics N2 - We propose an electro-mechanically coupled phase-field model for ferroelectric materials that show cubic–tetragonal phase transition. The cubic phase is idealized by an isotropic formulation, and the tetragonal phase is idealized by a transversely isotropic formulation. We consider a classical phase-field model with Ginzburg–Landau-type evolution of the order parameter. The order parameter drives the transition of all involved moduli tensors such as elastic, dielectric and piezoelectric moduli, which in turn maintain their typical features and stability as a result of a selected phase-transition function. The model is described in coordinate-invariant form and implemented into a finite element framework with implicit time integration of the evolution equation. Representative numerical examples in two and three dimensions demonstrate the main features of the constitutive model and the numerical stability of the formulation. KW - Phase-field modeling KW - Ferroelectrics KW - Ginzburg–Landau equation KW - Transverse isotropy KW - Numerical simulations Y1 - 2019 U6 - https://doi.org/10.1007/s00419-019-01543-y SN - 0939-1533 SN - 1432-0681 VL - 89 IS - 6 SP - 1057 EP - 1068 ER - TY - GEN A1 - Dornisch, Wolfgang A1 - Stöckler, Joachim A1 - Müller, Ralf T1 - Dual and approximate dual basis functions for B-splines and NURBS – Comparison and application for an efficient coupling of patches with the isogeometric mortar method T2 - Computer Methods in Applied Mechanics and Engineering N2 - This contribution defines and compares different methods for the computation of dual basis functions for B-splines and Non-Uniform Rational B-splines (NURBS). They are intended to be used as test functions for the isogeometric mortar method, but other fields of application are possible, too. Three different concepts are presented and compared. The first concept is the explicit formula for the computation of dual basis functions for NURBS proposed in the work of Carl de Boor. These dual basis functions entail minimal support, i.e., the support of the dual basis functions is equal to the support of the corresponding B-spline basis functions. In the second concept dual basis functions are derived from the inversion of the Gram matrix. These dual basis functions have global support along the interface. The third concept is the use of approximate dual basis functions, which were initially proposed for the use in harmonic analysis. The support of these functions is local but larger than the support of the associated B-spline basis functions. We propose an extension of the approximate dual basis functions for NURBS basis functions. After providing the general formulas, we elaborate explicit expressions for several degrees of spline basis functions. All three approaches are applied in the frame of the mortar method for the coupling of non-conforming NURBS patches. A method which allows complex discretizations with multiple intersecting interfaces is presented. Numerical examples show that the explicitly defined dual basis functions with minimal support severely deteriorate the global stress convergence behavior of the mechanical analysis. This fact is in accordance with mathematical findings in literature, which state that the optimal reproduction degree of arbitrary functions is not possible without extending the support of the dual basis functions. The dual basis functions computed from the inverse of the Gram matrix yield accurate numerical results but the global support yields significantly higher computational costs in comparison to computations of conforming meshes. Only the approximate dual basis functions yield accurate and efficient computations, where neither accuracy nor efficiency is significantly deteriorated in comparison to computations of conforming meshes. All basic cases of T-intersections and star-intersections are studied. Furthermore, an example which combines all basic cases in a complex discretization is given. The applicability of the presented method for the nonlinear case and for shell formulations is shown with the help of one numerical example. KW - Isogeometric analysis KW - Dual basis functions for NURBS KW - Optimal convergence KW - Mortar method KW - Coupling of non-conforming meshes KW - Approximate dual basis functions for NURBS Y1 - 2017 U6 - https://doi.org/10.1016/j.cma.2016.07.038 SN - 0045-7825 VL - 316 SP - 449 EP - 496 ER - TY - GEN A1 - Sobota, Paul M. A1 - Dornisch, Wolfgang A1 - Müller, Ralf A1 - Klinkel, Sven T1 - Implicit dynamic analysis using an iso- geometric Reissner–Mindlin shell formulation T2 - International Journal for Numerical Methods in Engineering N2 - In isogeometric analysis, identical basis functions are used for geometrical representation and analysis. In this work, non‐uniform rational basis splines basis functions are applied in an isoparametric approach. An isogeometric Reissner–Mindlin shell formulation for implicit dynamic calculations using the Galerkin method is presented. A consistent as well as a lumped matrix formulation is implemented. The suitability of the developed shell formulation for natural frequency analysis is demonstrated by a numerical example. In a second set of examples, transient problems of plane and curved geometries undergoing large deformations in combination with nonlinear material behavior are investigated. Via a zero‐thickness stress algorithm for arbitrary material models, a J2‐plasticity constitutive law is implemented. In the numerical examples, the effectiveness, robustness, and superior accuracy of a continuous interpolation method of the shell director vector is compared with experimental results and alternative numerical approaches. KW - isogeometric analysis KW - Reissner–Mindlin shell KW - NURBS KW - nonlinear material behavior KW - Structural vibrations KW - implicit dynamics KW - continuous director vector interpolation Y1 - 2017 U6 - https://doi.org/10.1002/nme.5429 SN - 1097-0207 VL - 110 IS - 9 SP - 803 EP - 825 ER - TY - GEN A1 - Dornisch, Wolfgang A1 - Müller, Ralf A1 - Klinkel, Sven T1 - An efficient and robust rotational formulation for isogeometric Reissner–Mindlin shell elements T2 - Computer Methods in Applied Mechanics and Engineering N2 - This work is concerned with the development of an efficient and robust isogeometric Reissner–Mindlin shell formulation for the mechanical simulation of thin-walled structures. Such structures are usually defined by non-uniform rational B-splines (NURBS) surfaces in industrial design software. The usage of isogeometric shell elements can avoid costly conversions from NURBS surfaces to other surface or volume geometry descriptions. The shell formulation presented in this contribution uses a continuous orthogonal rotation described by Rodrigues’ tensor in every integration point to compute the current director vector. The rotational state is updated in a multiplicative manner. Large deformations and finite rotations can be described accurately. The proposed formulation is robust in terms of stable convergence behavior in the nonlinear equilibrium iteration for large load steps and geometries with large and arbitrary curvature, and in terms of insensitivity to shell intersections with kinks under small angles. Three different integration schemes and their influence on accuracy and computational costs are assessed. The efficiency and robustness of the proposed isogeometric shell formulation is shown with the help of several examples. Accuracy and efficiency is compared to an isogeometric shell formulation with the more common discrete rotational concept and to Lagrange-based finite element shell formulations. The competitiveness of the proposed isogeometric shell formulation in terms of computational costs to attain a pre-defined error level is shown. KW - Isogeometric analysis KW - Geometrically nonlinear Reissner–Mindlin shell KW - NURBS KW - Interpolation of rotations KW - Numerical integration Y1 - 2016 U6 - https://doi.org/10.1016/j.cma.2016.01.018 SN - 0045-7825 VL - 303 SP - 1 EP - 34 ER - TY - GEN A1 - Dornisch, Wolfgang A1 - Müller, Ralf T1 - Modeling of electric field-induced magnetization switching in multi- ferroic heterostructures T2 - Proceedings in Applied Mathematics and Mechanics N2 - Multiferroic heterostructures consist of materials with either pronounced ferroelectric or ferromagnetic effect. The combination of both types of material, be it in layers, columns or inclusions, potentially yields a significant magneto‐electric coupling effect even at room temperature. The magnetization in the ferromagnetic material can be controlled by the application of electric fields to the ferroelectric material. In this contribution a linear elastic continuum formulation is coupled with a phase field formulation for the polarization and magnetization in the ferroelectric and the ferromagnetic layer, respectively. The strain transfer at the interface of the layers yields a magneto‐electric coupling effect within the heterostructures. The finite element method is used to discretize the arising differential equations. A numerical example provides a proof of concept for the simulation of the magneto‐electric coupling effect in multiferroic heterostructures. Y1 - 2019 U6 - https://doi.org/10.1002/pamm.201900103 SN - 1617-7061 VL - 19 IS - 1 ER -