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Technische Universität München
Technische Universität München

Computational Mechanics: Geometry and Numerical Simulation

In the Focus Group Computational Mechanics, Hans Fischer Fellow Prof. Alessandro Reali (Mechanics of Solids and Structures, Università di Pavia) collaborates with his host Prof. Ernst Rank (Computation in Engineering, TUM).

Over the last decade, the statement “geometry is the foundation of analysis” has been included among the basic principles of modern Computational Mechanics by an increasing number of researchers. However, from the practical point of view, geometry had so far limited impact on the field, the main reason being that Finite Element Analysis (FEA; i.e., the main engineering numerical analysis tool) was developed in the ‘50/’60's, well before the advent and widespread use of Computer Aided Geometric Design (CAGD; i.e., the main geometric design tool) which occurred only in the ‘70/’80's, and the connection between the two worlds relies on interfaces often far from efficient. As a result, building analysis-suitable geometries is estimated to take up to 80% of the overall analysis time for complex CAGD-based engineering designs. Moreover, since low order FEA methods are typically used, most meshes are made of simple geometrical objects like tetrahedra or hexahedra, which may not be able to represent highly sophisticated geometries with sufficient accuracy. Similar problems are present when the objects to be analyzed are obtained via imaging tools (in particular, in the medical field), and are further amplified when dealing with geometries evolving over time and involving the creation of new material, like in the case of Additive Manufacturing.

The above-mentioned low accuracy of classical FEA typically translates in very expensive simulations (and in some cases even to modeling errors and misleading results), and such a gap definitely has to be dealt with.

Isogeometric Analysis (IGA) was introduced in 2005 specifically aiming at bridging the gap between analysis and geometric design. The idea is to construct isoparametric methods based on splines (which are the basic ingredient of CAGD geometries) in order to make the construction of analysis-suitable geometries much simpler and more efficient. In addition, the higher continuity properties of splines often lead to increased efficiency in terms of approximation power and open the door to the development of new formulations based on higher order partial differential equations. The results have been so far much more than promising and IGA is now regarded as one of the most powerful Computational Mechanics tools, able to attract also industrial interests.

Another relevant and promising simulation framework is the recently developed Finite Cell Method (FCM), which allows to deal with very complex and/or evolving geometries in an incredibly simple and effective way (via the “immersed” concept). FCM can be easily combined with the IGA idea (and with spline functions), giving rise to very powerful and geometrically flexible computational tools.

Given these premises and also considering the fact that the Focus Group Members include some of the pioneers of the above mentioned methodologies, it seems natural to consider the combination of IGA and FCM as the way to go for creating efficient analysis tools for Additive Manufacturing problems, which constitute one of the most interesting modern challenges of Computational Mechanics.

Publications of the Focus Group

2019

  • Garoni, Carlo; Speleers, Hendrik; Ekström, Sven-Erik; Reali, Alessandro; Serra-Capizzano, Stefano; Hughes, Thomas J. R.: Symbol-Based Analysis of Finite Element and Isogeometric B-Spline Discretizations of Eigenvalue Problems: Exposition and Review. Archives of Computational Methods in Engineering, 2019 mehr…
  • Hoang, Tuong; Verhoosel, Clemens V.; Qin, Chao-Zhong; Auricchio, Ferdinando; Reali, Alessandro; van Brummelen, E. Harald: Skeleton-stabilized immersogeometric analysis for incompressible viscous flow problems. Computer Methods in Applied Mechanics and Engineering 344, 2019, 421-450 mehr…
  • Horger, Thomas; Reali, Alessandro; Wohlmuth, Barbara; Wunderlich, Linus: A hybrid isogeometric approach on multi-patches with applications to Kirchhoff plates and eigenvalue problems. Computer Methods in Applied Mechanics and Engineering 348, 2019, 396-408 mehr…
  • Lorenzo, Guillermo; Hughes, Thomas J. R.; Dominguez-Frojan, Pablo; Reali, Alessandro; Gomez, Hector: Computer simulations suggest that prostate enlargement due to benign prostatic hyperplasia mechanically impedes prostate cancer growth. Proceedings of the National Academy of Sciences 116 (4), 2019, 1152-1161 mehr…
  • Montanino, A.; Asprone, D.; Reali, A.; Auricchio, F.: A Least Square Residual version of the Modified Finite Particle Method to solve saddle point problems: Application to stationary Stokes and Navier–Stokes equations. International Journal of Mechanical Sciences 150, 2019, 176-187 mehr…
  • Romarowski, R.M.; Faggiano, E.; Conti, M.; Reali, A.; Morganti, S.; Auricchio, F.: A novel computational framework to predict patient-specific hemodynamics after TEVAR: Integration of structural and fluid-dynamics analysis by image elaboration. Computers & Fluids 179, 2019, 806-819 mehr…

2018

  • Campomenosi, Nicola; Mazzucchelli, Mattia L.; Mihailova, Boriana; Scambelluri, Marco; Angel, Ross J.; Nestola, Fabrizio; Reali, Alessandro; Alvaro, Matteo: How geometry and anisotropy affect residual strain in host-inclusion systems: Coupling experimental and numerical approaches. American Mineralogist 103 (12), 2018, 2032-2035 mehr…
  • Dufour, John-Eric; Antolin, Pablo; Sangalli, Giancarlo; Auricchio, Ferdinando; Reali, Alessandro: A cost-effective isogeometric approach for composite plates based on a stress recovery procedure. Composites Part B: Engineering 138, 2018, 12-18 mehr…
  • D’Angella, Davide; Kollmannsberger, Stefan; Rank, Ernst; Reali, Alessandro: Multi-level Bézier extraction for hierarchical local refinement of Isogeometric Analysis. Computer Methods in Applied Mechanics and Engineering 328, 2018, 147-174 mehr…
  • Evans, J.A.; Hiemstra, R.R.; Hughes, T.J.R.; Reali, A.: Explicit higher-order accurate isogeometric collocation methods for structural dynamics. Computer Methods in Applied Mechanics and Engineering 338, 2018, 208-240 mehr…
  • Hoang, Tuong; Verhoosel, Clemens V.; Auricchio, Ferdinando; van Brummelen, E. Harald; Reali, Alessandro: Skeleton-stabilized IsoGeometric Analysis: High-regularity interior-penalty methods for incompressible viscous flow problems. Computer Methods in Applied Mechanics and Engineering 337, 2018, 324-351 mehr…
  • Hosseini, Seyed Farhad; Hashemian, Ali; Reali, Alessandro: On the application of curve reparameterization in isogeometric vibration analysis of free-from curved beams. Computers & Structures 209, 2018, 117-129 mehr…
  • Morganti, S.; Callari, C.; Auricchio, F.; Reali, A.: Mixed isogeometric collocation methods for the simulation of poromechanics problems in 1D. Meccanica 53 (6), 2018, 1441-1454 mehr…
  • Xu, Fei; Morganti, Simone; Zakerzadeh, Rana; Kamensky, David; Auricchio, Ferdinando; Reali, Alessandro; Hughes, Thomas J. R.; Sacks, Michael S.; Hsu, Ming-Chen: A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis. International Journal for Numerical Methods in Biomedical Engineering 34 (4), 2018, e2938 mehr…

2017

  • Balduzzi, Giuseppe; Morganti, Simone; Auricchio, Ferdinando; Reali, Alessandro: Non-prismatic Timoshenko-like beam model: Numerical solution via isogeometric collocation. Computers & Mathematics with Applications 74 (7), 2017, 1531-1541 mehr…
  • Bas, Onur; De-Juan-Pardo, Elena M; Meinert, Christoph; D’Angella, Davide; Baldwin, Jeremy G; Bray, Laura J; Wellard, R Mark; Kollmannsberger, Stefan; Rank, Ernst; Werner, Carsten; Klein, Travis J; Catelas, Isabelle; Hutmacher, Dietmar W: Biofabricated soft network composites for cartilage tissue engineering. Biofabrication 9 (2), 2017, 025014 mehr…
  • Bas, Onur; D’Angella, Davide; Baldwin, Jeremy G.; Castro, Nathan J.; Wunner, Felix M.; Saidy, Navid T.; Kollmannsberger, Stefan; Reali, Alessandro; Rank, Ernst; De-Juan-Pardo, Elena M.; Hutmacher, Dietmar W.: An Integrated Design, Material, and Fabrication Platform for Engineering Biomechanically and Biologically Functional Soft Tissues. ACS Applied Materials & Interfaces 9 (35), 2017, 29430-29437 mehr…
  • Bog, Tino; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst: Weak imposition of frictionless contact constraints on automatically recovered high-order, embedded interfaces using the finite cell method. Computational Mechanics 61 (4), 2017, 385-407 mehr…
  • Casquero, Hugo; Liu, Lei; Zhang, Yongjie; Reali, Alessandro; Kiendl, Josef; Gomez, Hector: Arbitrary-degree T-splines for isogeometric analysis of fully nonlinear Kirchhoff–Love shells. Computer-Aided Design 82, 2017, 140-153 mehr…
  • Heltai, Luca; Kiendl, Josef; DeSimone, Antonio; Reali, Alessandro: A natural framework for isogeometric fluid–structure interaction based on BEM–shell coupling. Computer Methods in Applied Mechanics and Engineering 316, 2017, 522-546 mehr…
  • Hoang, Tuong; Verhoosel, Clemens V.; Auricchio, Ferdinando; van Brummelen, E. Harald; Reali, Alessandro: Mixed Isogeometric Finite Cell Methods for the Stokes problem. Computer Methods in Applied Mechanics and Engineering 316, 2017, 400-423 mehr…
  • Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander: Numerical integration of discontinuous functions: moment fitting and smart octree. Computational Mechanics 60 (5), 2017, 863-881 mehr…
  • Jomo, John N.; Zander, Nils; Elhaddad, Mohamed; Özcan, Ali; Kollmannsberger, Stefan; Mundani, Ralf-Peter; Rank, Ernst: Parallelization of the multi-levelhp-adaptive finite cell method. Computers & Mathematics with Applications 74 (1), 2017, 126-142 mehr…
  • Kiendl, J.; Auricchio, F.; Reali, A.: A displacement-free formulation for the Timoshenko beam problem and a corresponding isogeometric collocation approach. Meccanica 53 (6), 2017, 1403-1413 mehr…
  • Montanino, A.; Asprone, D.; Reali, A.; Auricchio, F.: Modified Finite Particle Methods for Stokes problems. Computational Particle Mechanics 5 (2), 2017, 141-160 mehr…
  • Niiranen, Jarkko; Kiendl, Josef; Niemi, Antti H.; Reali, Alessandro: Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates. Computer Methods in Applied Mechanics and Engineering 316, 2017, 328-348 mehr…
  • Paolini, Alexander; Kollmannsberger, Stefan; Winter, Christoph; Buchschmid, Martin; Müller, Gerhard; Rabold, Andreas; Mecking, Simon; Schanda, Ulrich; Rank, Ernst: A high-order finite element model for vibration analysis of cross-laminated timber assemblies. Building Acoustics 24 (3), 2017, 135-158 mehr…
  • Perotto, S.; Reali, A.; Rusconi, P.; Veneziani, A.: HIGAMod: A Hierarchical IsoGeometric Approach for MODel reduction in curved pipes. Computers & Fluids 142, 2017, 21-29 mehr…
  • Ranjbar, M.; Mashayekhi, M.; Parvizian, J.; Düster, A.; Rank, E.: Finite Cell Method implementation and validation of a nonlocal integral damage model. International Journal of Mechanical Sciences 128-129, 2017, 401-413 mehr…
  • Seidl, Robert; Rank, Ernst: Full waveform inversion for ultrasonic flaw identification. , Author(s), 2017 mehr…
  • Wassermann, Benjamin; Kollmannsberger, Stefan; Bog, Tino; Rank, Ernst: From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry. Computers & Mathematics with Applications 74 (7), 2017, 1703-1726 mehr…

2016

  • Auricchio, F; Ferretti, M; Lefieux, A; Musci, M; Reali, A; Trimarchi, S; Veneziani, A: Parallelizing a finite element solver in computational hemodynamics. The International Journal of High Performance Computing Applications 32 (3), 2016, 351-362 mehr…
  • Auricchio, Ferdinando; Boatti, Elisa; Reali, Alessandro; Stefanelli, Ulisse: Gradient structures for the thermomechanics of shape-memory materials. Computer Methods in Applied Mechanics and Engineering 299, 2016, 440-469 mehr…
  • Casquero, Hugo; Liu, Lei; Zhang, Yongjie; Reali, Alessandro; Gomez, Hector: Isogeometric collocation using analysis-suitable T-splines of arbitrary degree. Computer Methods in Applied Mechanics and Engineering 301, 2016, 164-186 mehr…
  • Conti, Michele; Long, Chris; Marconi, Michele; Berchiolli, Raffaella; Bazilevs, Yuri; Reali, Alessandro: Carotid artery hemodynamics before and after stenting: A patient specific CFD study. Computers & Fluids 141, 2016, 62-74 mehr…
  • Conti, Michele; Marconi, Michele; Campanile, Giulia; Reali, Alessandro; Adami, Daniele; Berchiolli, Raffaella; Auricchio, Ferdinando: Patient-specific finite element analysis of popliteal stenting. Meccanica 52 (3), 2016, 633-644 mehr…
  • D’Angella, Davide; Zander, Nils; Kollmannsberger, Stefan; Frischmann, Felix; Rank, Ernst; Schröder, Andreas; Reali, Alessandro: Multi-level hp-adaptivity and explicit error estimation. Advanced Modeling and Simulation in Engineering Sciences 3 (1), 2016 mehr…
  • Gallo, Diego; Lefieux, Adrien; Morganti, Simone; Veneziani, Alessandro; Reali, Alessandro; Auricchio, Ferdinando; Conti, Michele; Morbiducci, Umberto: A patient-specific follow up study of the impact of thoracic endovascular repair (TEVAR) on aortic anatomy and on post-operative hemodynamics. Computers & Fluids 141, 2016, 54-61 mehr…
  • Kiendl, Josef; Ambati, Marreddy; De Lorenzis, Laura; Gomez, Hector; Reali, Alessandro: Phase-field description of brittle fracture in plates and shells. Computer Methods in Applied Mechanics and Engineering 312, 2016, 374-394 mehr…
  • Kudela, László; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst: Smart octrees: Accurately integrating discontinuous functions in 3D. Computer Methods in Applied Mechanics and Engineering 306, 2016, 406-426 mehr…
  • Morganti, S.; Brambilla, N.; Petronio, A.S.; Reali, A.; Bedogni, F.; Auricchio, F.: Prediction of patient-specific post-operative outcomes of TAVI procedure: The impact of the positioning strategy on valve performance. Journal of Biomechanics 49 (12), 2016, 2513-2519 mehr…
  • Seidl, Robert; Rank, Ernst: Iterative time reversal based flaw identification. Computers & Mathematics with Applications 72 (4), 2016, 879-892 mehr…
  • Wille, Hagen; Ruess, Martin; Rank, Ernst; Yosibash, Zohar: Uncertainty quantification for personalized analyses of human proximal femurs. Journal of Biomechanics 49 (4), 2016, 520-527 mehr…
  • Zander, Nils; Bog, Tino; Elhaddad, Mohamed; Frischmann, Felix; Kollmannsberger, Stefan; Rank, Ernst: The multi-levelhp-method for three-dimensional problems: Dynamically changing high-order mesh refinement with arbitrary hanging nodes. Computer Methods in Applied Mechanics and Engineering 310, 2016, 252-277 mehr…

2015

  • Asprone, D.; Auricchio, F.; Montanino, A.; Reali, A.: Review of the modified finite particle method and application to incompressible solids. The International Journal of Multiphysics 9 (3), 2015, 235-248 mehr…
  • Auricchio, F.; Conti, M.; Ferraro, M.; Morganti, S.; Reali, A.; Taylor, R.L.: Innovative and efficient stent flexibility simulations based on isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 295, 2015, 347-361 mehr…
  • Auricchio, Ferdinando; Lefieux, Adrien; Reali, Alessandro; Veneziani, Alessandro: A locally anisotropic fluid-structure interaction remeshing strategy for thin structures with application to a hinged rigid leaflet. International Journal for Numerical Methods in Engineering 107 (2), 2015, 155-180 mehr…
  • Auricchio, Ferdinando; Veiga, Lourenco Beirão da; Kiendl, Josef; Lovadina, Carlo; Reali, Alessandro: Isogeometric collocation mixed methods for rods. Discrete and Continuous Dynamical Systems - Series S 9 (1), 2015, 33-42 mehr…
  • Bog, Tino; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst: Normal contact with high order finite elements and a fictitious contact material. Computers & Mathematics with Applications 70 (7), 2015, 1370-1390 mehr…
  • Dauge, Monique; Düster, Alexander; Rank, Ernst: Theoretical and Numerical Investigation of the Finite Cell Method. Journal of Scientific Computing 65 (3), 2015, 1039-1064 mehr…
  • Elhaddad, M.; Zander, N.; Kollmannsberger, S.; Shadavakhsh, A.; Nübel, V.; Rank, E.: Finite Cell Method: High-Order Structural Dynamics for Complex Geometries. International Journal of Structural Stability and Dynamics 15 (07), 2015, 1540018 mehr…
  • Ferraro, Mauro; Auricchio, Ferdinando; Boatti, Elisa; Scalet, Giulia; Conti, Michele; Morganti, Simone; Reali, Alessandro: An Efficient Finite Element Framework to Assess Flexibility Performances of SMA Self-Expandable Carotid Artery Stents. Journal of Functional Biomaterials 6 (3), 2015, 585-597 mehr…
  • Kiendl, Josef; Hsu, Ming-Chen; Wu, Michael C.H.; Reali, Alessandro: Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials. Computer Methods in Applied Mechanics and Engineering 291, 2015, 280-303 mehr…
  • Kudela, László; Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Rank, Ernst: Efficient and accurate numerical quadrature for immersed boundary methods. Advanced Modeling and Simulation in Engineering Sciences 2 (1), 2015 mehr…
  • Manni, Carla; Reali, Alessandro; Speleers, Hendrik: Isogeometric collocation methods with generalized B-splines. Computers & Mathematics with Applications 70 (7), 2015, 1659-1675 mehr…
  • Yosibash, Zohar; Wille, Hagen; Rank, Ernst: Stochastic description of the peak hip contact force during walking free and going upstairs. Journal of Biomechanics 48 (6), 2015, 1015-1022 mehr…
  • Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Schillinger, Dominik; Rank, Ernst: Multi-level hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes. Computational Mechanics 55 (3), 2015, 499-517 mehr…
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