@misc{DornischSchradeXuetal., author = {Dornisch, Wolfgang and Schrade, David and Xu, Bai-Xiang and M{\"u}ller, Ralf}, title = {Coupling of phase field models for ferroelectric and ferromagnetic layers in multiferroic heterostructures}, series = {VII International Conference on Coupled Problems in Science and Engineering (Coupled Problems 2017)}, journal = {VII International Conference on Coupled Problems in Science and Engineering (Coupled Problems 2017)}, publisher = {CIMNE}, address = {Barcelona}, pages = {1}, abstract = {Heterostructures of ferroelectric and ferromagnetic layers are commonly used to obtain electromagnetic effects. The elastic coupling between the layers is widely acknowledged as the main mechanism responsible for the electro-magneto interaction. Within this contribution we study the coupling of ferroelectric and ferromagnetic layers with well-defined interfaces. The intention is to simulate the switching of the magnetization with the help of electric fields, which has been studied experimentally in [1]. Each layer is simulated by using mechanically coupled phase field modeling, whereby the approaches presented in [2] and [3] will be used. The strains in each layer depend on the direction of the polarization/magnetization. A mismatch of these strains will be compensated by local deformations at the interface as the coupling results from the coherent deformation at the interface. This leads to the possibility to alter the magnetization direction by changing the electric polarization and vice verse. Numerical simulations will illustrate the evolution of the ferroic microstructures with a focus on the strain coupling and the resulting interactions between layers.}, language = {en} } @misc{DornischMueller, author = {Dornisch, Wolfgang and M{\"u}ller, Ralf}, title = {Phase field modelling of ferroelectric-ferromagnetic interfaces}, series = {Proceedings of the Third Seminar on The Mechanics of Multifunctional Materials : Physikzentrum Bad Honnef June 11 - 15, 2018}, journal = {Proceedings of the Third Seminar on The Mechanics of Multifunctional Materials : Physikzentrum Bad Honnef June 11 - 15, 2018}, editor = {Schr{\"o}der, J{\"o}rg and Lupascu, Doru C. and Wende, Heiko and Brands, Dominik}, publisher = {Universit{\"a}t Duisburg-Essen}, address = {Essen}, isbn = {3-9818074-4-8}, doi = {10.17185/duepublico/46481}, url = {http://nbn-resolving.de/urn:nbn:de:hbz:464-20180702-085433-3}, pages = {93 -- 96}, abstract = {Magneto-electric coupling along interfaces between ferroelectric and ferromagneticmaterials allows the magnetization in ferromagnetic layers to be controlled by electrical fields.The coupling effect is mainly due to the deformation coupling between the layers. Thus, furthercoupling effects at the interfaces are neglected in this contribution. Phase field formulationsare used to model the polarization and magnetization in the ferroelectric and ferromagneticlayers, respectively. A coupling between the phase field and the strains is introduced in eachlayer in combination with a mechanical coupling at the interface. The numerical formulationfor the ferroelectric layer is taken from literature. A special focus is set on the discretization ofthe length-constrained order parameter in the ferromagnetic layer. We show a new approachto enforce this constraint and provide a numerical simulation which illustrates the magneto-electric coupling effect.}, language = {en} } @misc{Dornisch, author = {Dornisch, Wolfgang}, title = {Efficient Integration Schemes in NURBS-based Isogeometric Analysis - Comparison and Application to Shell Elements}, series = {VII International Conference on Isogeometric Analysis}, journal = {VII International Conference on Isogeometric Analysis}, publisher = {CIMNE}, address = {Barcelona}, pages = {1}, abstract = {The efficiency of the NURBS-based isogeometric Galerkin method highly depends on the chosen numerical integration scheme for the evaluation of the stiffness matrix and the residual vector. In an efficient implementation, the computational costs for the formation of the stiffness matrix scale almost linearly with the total number of integration points. Furthermore, also the accuracy of the solution depends on the chosen integration scheme, since spurious locking effects increase with the number of integration points. Gauss integration is probably the most common approach for numerical integration in NURBS-based IGA, whereby the higher continuity in IGA can be exploited for a reduction of the number of integration points, see [2]. More sophisticated integration schemes have been proposed in [3,4], where a nonlinear equation is solved in order to compute integration weights and quadrature points. Using the minimum possible number of quadrature points, the nonlinear equation aims at integrating the univariate B-spline spaces exactly. Thus, the methods can be considered as optimal. In this contribution, an implementation of the optimal integration method [3] for general NURBS surfaces with non-uniform knot vectors is presented. The integration method is applied to the Poisson problem, two-dimensional plane stress problems and isogeometric shell elements as proposed in [5]. The numerical examples of this study focus on the accuracy of the integration for NURBS surfaces with non-uniform weights. A further very important aspect is the comparison of computational costs between the different methods. The alleviation of locking effects, which comes along with a reduction of the number of integration points, is studied for the shell elements proposed in [5]. Furthermore, a comparison to the locking-free formulation of [6] is given.}, language = {en} } @misc{ChasapiDornischKlinkel, author = {Chasapi, Margarita and Dornisch, Wolfgang and Klinkel, Sven}, title = {Coupling of patches for isogeometric analysis of solids in boundary representation}, series = {VII International Conference on Isogeometric Analysis}, journal = {VII International Conference on Isogeometric Analysis}, publisher = {CIMNE}, address = {Barcelona}, pages = {1}, abstract = {In this contribution we present a coupling approach for non-conforming NURBS patches in the framework of an isogeometric formulation in boundary representation [1]. In order to fit the boundary representation modeling technique in CAD, we follow the idea of the scaled boundary finite element method [2] for the parameterization of the solid. Thus, two-dimensional solid surfaces are partitioned into sections in relation to a central point, the scaling center. Each section is parameterized with a circumferential parameter along the boundary and a radial scaling parameter in the interior of the domain. We employ NURBS basis functions for the approximation of the solution in both parametric directions. The approximation in scaling direction is flexible and allows for local refinement within the computational domain. For the coupling of non-conforming sections we employ a mortar approach as presented in [3]. We establish a master-slave relation for the interface control points between adjacent sections based on the equality of mutual deformations along the interface. The coupling is realized in a weak manner by constraining the basis functions, which means that the NURBS basis functions of the slave side are related to those of the master side so that the solution of both sections along the interface is equal in a weak sense. This approach is derived numerically and its application to nonlinear problems is straightforward. We study several numerical examples of linear and nonlinear problems in solid mechanics and compare the results with conforming computations.}, language = {en} } @misc{DornischSchradeWolfetal., author = {Dornisch, Wolfgang and Schrade, David and Wolf, Jana and M{\"u}ller, Ralf}, title = {Numerical methods for the modeling of the magnetization vector in multiferroic heterostructures}, series = {Proceedings in Applied Mathematics and Mechanics, Special Issue: 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017)}, volume = {17}, journal = {Proceedings in Applied Mathematics and Mechanics, Special Issue: 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017)}, number = {1}, publisher = {WILEY-VCH Verlag GmbH \& Co. KGaA}, address = {Weinheim}, issn = {1617-7061}, doi = {10.1002/pamm.201710221}, pages = {503 -- 504}, abstract = {Multiferroic heterostructures are commonly used to obtain electro-magnetic coupling effects. Thereby, the ferroelectric layer is used to control the magnetization in the ferromagnetic layer. The coupling between the layers is obtained by the mechanical coupling between the layers, which have well-defined interfaces. Within this contribution we use phase field models to define the polarization and magnetization in the ferroelectric and ferromagnetic layers, respectively. A coupling between polarization/magnetization and strains in each layer in combination with coherent deformations at the interface yields an electromagnetic coupling within the entire heterostructure. Numerical formulations for the interpolation of the polarization vector are well-defined in the literature. However, the establishment of a consistent numerical formulation for the ferromagnetic layer, where the length of the magnetization vector has to be constant, remains a difficult task. We propose a new numerical approach for the consistent treatment of the ferromagnetic layer and provide numerical simulations which illustrate the electromagnetic coupling effect.}, language = {en} } @misc{DornischYan, author = {Dornisch, Wolfgang and Yan, Sikang}, title = {Effiziente Integrationsmethoden f{\"u}r isogeometrische Schalenelemente}, series = {Berichte der Fachtagung Baustatik - Baupraxis 14}, journal = {Berichte der Fachtagung Baustatik - Baupraxis 14}, editor = {Bischoff, Manfred and Scheven, Malte von and Oesterle, Bastian}, publisher = {Institut f{\"u}r Baustatik und Baudynamik, Universit{\"a}t Stuttgart}, address = {Stuttgart}, isbn = {978-3-00-064639-3}, doi = {10.18419/opus-10762}, url = {http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-107793}, pages = {415 -- 422}, abstract = {Die isogeometrische Methode definiert sich durch den Einsatz einer einheitlichen Geometriebeschreibung f{\"u}r Entwurf und Berechnung. Insbesondere bei der Berechnung d{\"u}nnwandiger Fl{\"a}chentragwerke ist durch die Verwendung der exakten Geometrie ein großer Gewinn an Genauigkeit und Zuverl{\"a}ssigkeit m{\"o}glich. Um neben hoher Genauigkeit auch hohe Effizienz zu erreichen, wird in diesem Beitrag die Verwendung effizienter numerischer Integrationsmethoden f{\"u}r die Berechnung der Steifigkeitsmatrix untersucht.}, language = {de} } @misc{ChasapiDornischKlinkel, author = {Chasapi, Margarita and Dornisch, Wolfgang and Klinkel, Sven}, title = {Patch coupling in isogeometric analysis of solids inboundary representation using a mortar approach}, series = {International Journal for Numerical Methods in Engineering}, volume = {121}, journal = {International Journal for Numerical Methods in Engineering}, number = {14}, issn = {1097-0207}, doi = {10.1002/nme.6354}, pages = {3206 -- 3226}, abstract = {This contribution is concerned with a coupling approach for nonconforming NURBS patches in the framework of an isogeometric formulation for solids inboundary representation. The boundary representation modeling technique inCAD is the starting point of this approach. We parameterize the solid according to the scaled boundary finite element method and employ NURBS basis functions for the approximation of the solution. Therefore, solid surfaces consist of several sections, which can be regarded as patches and discretized independently. The main objective of this study is to derive an approach for the connection of independent sections in order to allow for local refinement and thus an accurate and efficient discretization of the computational domain. Non-conforming sections are coupled with a mortar approach within a master-slave framework. The coupling of adjacent sections ensures the equality of mutual deformations along the interface in a weak sense and is enforced by constraining the NURBS basis functions on the interface. We apply this approach to non-linear problems in two dimensions and compare the results with conforming discretizations.}, language = {en} } @misc{ZouScottMiaoetal., author = {Zou, Zhihui and Scott, Michael A. and Miao, Di and Bischoff, Manfred and Oesterle, Bastian and Dornisch, Wolfgang}, title = {An isogeometric Reissner-Mindlin shell element based on B{\´e}zier dual basis functions: Overcoming locking and improved coarse mesh accuracy}, series = {Computer Methods in Applied Mechanics and Engineering}, volume = {370}, journal = {Computer Methods in Applied Mechanics and Engineering}, issn = {0045-7825}, doi = {10.1016/j.cma.2020.113283}, pages = {35}, abstract = {We develop a mixed geometrically nonlinear isogeometric Reissner-Mindlin shell element for the analysis of thin-walled structures that leverages B{\´e}zier dual basis functions to address both shear and membrane locking and to improve the quality of computed stresses. The accuracy of computed solutions over coarse meshes, that have highly non-interpolatory control meshes, is achieved through the application of a continuous rotational approach. The starting point of the formulation is the modified Hellinger-Reissner variational principle with independent displacement, membrane, and shear strains as the unknown fields. To overcome locking, the strain variables are interpolated with lower-order spline bases while the variations of the strain variables are interpolated with the corresponding B{\´e}zier dual bases. Leveraging the orthogonality property of the B{\´e}zier dual basis, the strain variables are condensed out of the system with only a slight increase in the bandwidth of the resulting linear system. The condensed approach preserves the accuracy of the non-condensed mixed approach but with fewer degrees of freedom. From a practical point of view, since the B{\´e}zier dual basis is completely specified through B{\´e}zier extraction, any spline space that admits B{\´e}zier extraction can utilize the proposed approach directly.}, language = {en} } @misc{AzizAliYanDornischetal., author = {Aziz Ali, Sk and Yan, Sikang and Dornisch, Wolfgang and Stricker, Didier}, title = {Foldmatch: Accurate and High Fidelity Garment Fitting Onto 3D Scans}, series = {2020 IEEE International Conference on Image Processing (ICIP)}, journal = {2020 IEEE International Conference on Image Processing (ICIP)}, address = {Abu Dhabi, United Arab Emirates}, isbn = {978-1-7281-6395-6}, issn = {2381-8549}, doi = {10.1109/ICIP40778.2020.9190730}, pages = {5}, abstract = {In this paper, we propose a new template fitting method that can capture fine details of garments in target 3D scans of dressed human bodies. Matching the high fidelity details of such loose/tight-fit garments is a challenging task as they express intricate folds, creases, wrinkle patterns, and other high fidelity surface details. Our proposed method of non-rigid shape fitting - FoldMatch - uses physics-based particle dynamics to explicitly model the deformation of loose-fit garments and wrinkle vector fields for capturing clothing details. The 3D scan point cloud behaves as a collection of astrophysical particles, which attracts the points in template mesh and defines the template motion model. We use this point-based motion model to derive regularized deformation gradients for the template mesh. We show the parameterization of the wrinkle vector fields helps in the accurate shape fitting. Our method shows better performance than the stateof-the-art methods. We define several deformation and shape matching quality measurement metrics to evaluate FoldMatch on synthetic and real data sets.}, language = {en} } @misc{SchmidtAmmarDornischetal., author = {Schmidt, Simon David and Ammar, Kais and Dornisch, Wolfgang and Forest, Samuel and M{\"u}ller, Ralf}, title = {Phase field model for the martensitic transformation: comparison of the Voigt/Taylor and Khachaturyan approach}, series = {Continuum Mechanics and Thermodynamics}, volume = {33}, journal = {Continuum Mechanics and Thermodynamics}, number = {5}, issn = {0935-1175}, doi = {10.1007/s00161-021-01007-1}, pages = {2075 -- 2094}, language = {en} } @misc{DornischStoeckler, author = {Dornisch, Wolfgang and St{\"o}ckler, Joachim}, title = {An isogeometric mortar method for the coupling of multiple NURBS domains with optimal convergence rates}, series = {Numerische Mathematik}, volume = {149}, journal = {Numerische Mathematik}, number = {4}, issn = {0945-3245}, doi = {10.1007/s00211-021-01246-z}, pages = {871 -- 931}, abstract = {We investigate the mortar finite element method for second order elliptic boundary value problems on domains which are decomposed into patchesk with tensor-product NURBS parameterizations. We follow the methodology of IsoGeometric Analysis (IGA) and choose discrete spaces Xh,k on each patch k as tensor-product NURBS spaces of the same or higher degree as given by the parameterization. Our work is an extension of Brivadis et al. (Comput Methods Appl Mech Eng 284:292-319, 2015) and highlights several aspects which did not receive full attention before. In particular, by choosing appropriate spaces of polynomial splines as Lagrange multipliers, we obtain a uniform infsup-inequality. Moreover, we provide a new additional condition on the discrete spaces Xh,k which is required for obtaining optimal convergence rates of the mortar method. Our numerical examples demonstrate that the optimal rate is lost if this condition is neglected.}, language = {en} } @misc{HeldDornisch, author = {Held, Susanne and Dornisch, Wolfgang}, title = {Mass lumping scheme for IGA dynamics}, series = {11th European Solid Mechanics Conference}, journal = {11th European Solid Mechanics Conference}, address = {Galway, Irland}, pages = {1}, abstract = {The aim of this study is to provide a new mass lumping scheme for explicit dynamic calculations in isogeometric analysis (IGA). Shape functions for IGA methods are taken from the Computer-Aided design (CAD) model. The use of higher-order polynomials, usually Non-Uniform Rational B-Splines (NURBS), ensures an exact geometry description [1]. Thus, in comparison to standard finite element method (FEM) the number of elements and therefore the computational costs can be lowered. In addition to that the convergence rate raises equally with the polynomial order. Increasing the degree of shape functions, less elements are necessary for results of the same quality. In explicit dynamics, mass lumping schemes are commonly applied to reduce computational costs by using diagonal mass matrices. Well-known techniques like row-sum lumping or diagonal scaling method were developed for dynamic analysis with standard FEM. Unfortunately, they are neither suitable for higher-order shape functions in IGA, nor in the spectral element method [2]. It is not possible to take advantage of increasing the polynomial order to lower the number of elements in explicit dynamic IGA, because the error caused by lumping the mass matrix also increases. Thus, other mass lumping schemes, suitable for higher-order shape functions, have to be developed. As they are already used for isogeometric mortar method [3], several types of dual basis functions (duals) are studied for a new mass lumping scheme. Using duals as test functions in IGA leads to diagonal consistent mass matrices [4] or banded matrices, depending on the chosen type of duals. In case of the banded matrices, additional row-sum lumping causes smaller errors than lumping the original mass matrix with standard NURBS as test functions. For IGA dynamics with explicit time integration, e.g. the Central Difference Method, using duals as test functions is a very promising approach. They can be easily implemented in existing methods through multiplying the already assembled system matrices with a transformation matrix based on the underlying NURBS curve. Applying the dual lumping scheme, an explicit dynamic analysis could also be performed efficiently using IGA methods with higher-order shape functions.}, language = {en} } @misc{StammenDornisch, author = {Stammen, Lisa and Dornisch, Wolfgang}, title = {Investigations on the use of adapted approximation orders for a convective IGA formulation}, series = {11th European Solid Mechanics Conference}, journal = {11th European Solid Mechanics Conference}, address = {Galway, Irland}, pages = {1}, abstract = {In isogeometric analysis (IGA), which was founded by Hughes et al. [1], the geometry representation is used for the analysis as well. Hence, due to the exact description of the geometry, analysis results can be improved [1, 2]. Therefore, different kinds of splines, like non-uniform rational B-splines (NURBS) [3], are used as shape functions for the discretizations. In linear elasticity problems, for standard formulations, shear locking phenomena can occur due to the different orders of the derivatives in the unbalanced strain-displacement relation. This effect can be reduced using shape functions of higher order, causing an increased computational effort. For low-order formulations, the degrees of shape functions can be adapted accordingly in order to counteract this effect. For an isogeometric displacement-stress mixed Reissner-Mindlin shell formulation such adapted approximation spaces were investigated in [4], for instance. In [5], additionally to a proper choice of shape function spaces, convective coordinates are employed in the derivation of isogeometric shell formulations. In this contribution, a convective displacement-based isogeometric formulation is introduced, wherein the displacements in the different surface directions are approximated independently using appropriate approximation orders. Therefore, two different meshes are generated from the NURBSdescribed geometry representation, employing order elevation solely for one of the two surface directions. Thus, the order is elevated in opposite directions for these two meshes. The two different possibilities of order elevation are investigated. Furthermore, the use of different convective basis systems is studied. This comprises convective basis systems in each control point, computed according to [6], as well as convective basis systems determined from the local geometry direction in each integration point. The achieved results are compared to whose of a two-dimensional displacementstress mixed formulation presented in [7].}, language = {en} }