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Non-standard Discretisation Methods in Solid Mechanics

  • Book
  • © 2022

Overview

Editors:
  1. Jörg Schröder

    1. Institute of Mechanics, University of Duisburg-Essen, Essen, Germany

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  2. Peter Wriggers

    1. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

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    You can also search for this editor in PubMed   Google Scholar

  • Summarizes recent advances in finite element technologies
  • Focuses on modern phase-field approaches to fracture
  • Written by leading experts in the field

Part of the book series: Lecture Notes in Applied and Computational Mechanics (LNACM, volume 98)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-viii
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  2. Hybrid Discretizations in Solid Mechanics for Non-linear and Non-smooth Problems

    • H. R. Bayat, J. Krämer, S. Reese, C. Wieners, B. Wohlmuth, L. Wunderlich
    Pages 1-35

  3. Novel Finite Elements - Mixed, Hybrid and Virtual Element Formulations at Finite Strains for 3D Applications

    • Jörg Schröder, Peter Wriggers, Alex Kraus, Nils Viebahn
    Pages 37-67

  4. Robust and Efficient Finite Element Discretizations for Higher-Order Gradient Formulations

    • Johannes Riesselmann, Jonas Wilhelm Ketteler, Mira Schedensack, Daniel Balzani
    Pages 69-90

  5. Stress Equilibration for Hyperelastic Models

    • F. Bertrand, M. Moldenhauer, G. Starke
    Pages 91-105

  6. Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods

    • Philipp Bringmann, Carsten Carstensen, Ngoc Tien Tran
    Pages 107-147

  7. Least-Squares Finite Element Formulation for Finite Strain Elasto-Plasticity

    • M. Igelbüscher, J. Schröder, A. Schwarz, G. Starke
    Pages 149-167

  8. Hybrid Mixed Finite Element Formulations Based on a Least-Squares Approach

    • Maximilian Igelbüscher, Jörg Schröder
    Pages 169-189

  9. Adaptive and Pressure-Robust Discretization of Incompressible Pressure-Driven Phase-Field Fracture

    • Seshadri Basava, Katrin Mang, Mirjam Walloth, Thomas Wick, Winnifried Wollner
    Pages 191-215

  10. A Phase-Field Approach to Pneumatic Fracture

    • C. Bilgen, A. Kopaničáková, R. Krause, K. Weinberg
    Pages 217-241

  11. Adaptive Isogeometric Phase-Field Modeling of Weak and Strong Discontinuities

    • Paul Hennig, Markus Kästner, Roland Maier, Philipp Morgenstern, Daniel Peterseim
    Pages 243-282

  12. Phase Field Modeling of Brittle and Ductile Fracture

    • Charlotte Kuhn, Timo Noll, Darius Olesch, Ralf Müller
    Pages 283-325

  13. Adaptive Quadrature and Remeshing Strategies for the Finite Cell Method at Large Deformations

    • Wadhah Garhuom, Simeon Hubrich, Lars Radtke, Alexander Düster
    Pages 327-353

  14. The Finite Cell Method for Simulation of Additive Manufacturing

    • Stefan Kollmannsberger, Davide D’Angella, Massimo Carraturo, Alessandro Reali, Ferdinando Auricchio, Ernst Rank
    Pages 355-375

  15. Error Control and Adaptivity for the Finite Cell Method

    • Paolo Di Stolfo, Andreas Schröder
    Pages 377-403

  16. Frontiers in Mortar Methods for Isogeometric Analysis

    • Christian Hesch, Ustim Khristenko, Rolf Krause, Alexander Popp, Alexander Seitz, Wolfgang Wall et al.
    Pages 405-447

  17. Collocation Methods and Beyond in Non-linear Mechanics

    • F. Fahrendorf, S. Shivanand, B. V. Rosic, M. S. Sarfaraz, T. Wu, L. De Lorenzis et al.
    Pages 449-504

  18. Approximation Schemes for Materials with Discontinuities

    • Sören Bartels, Marijo Milicevic, Marita Thomas, Sven Tornquist, Nico Weber
    Pages 505-565
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Keywords

About this book

This edited volume summarizes research being pursued within the DFG Priority Programme 1748: "Reliable Simulation Methods in Solid Mechanics. Development of non-standard discretisation methods, mechanical and mathematical analysis", the aim of which was to develop novel discretisation methods based e.g. on mixed finite element methods, isogeometric approaches as well as discontinuous Galerkin formulations, including a sound mathematical analysis for geometrically as well as physically nonlinear problems. The Priority Programme has established an international framework for mechanical and applied mathematical research to pursue open challenges on an inter-disciplinary level. The compiled results can be understood as state of the art in the research field and show promising ways of further research in the respective areas. The book is intended for doctoral and post-doctoral students in civil engineering, mechanical engineering, applied mathematics and physics, as well as industrial researchers interested in the field.

Editors and Affiliations

  • Institute of Mechanics, University of Duisburg-Essen, Essen, Germany

    Jörg Schröder

  • Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers

Bibliographic Information

  • Book Title: Non-standard Discretisation Methods in Solid Mechanics

  • Editors: Jörg Schröder, Peter Wriggers

  • Series Title: Lecture Notes in Applied and Computational Mechanics

  • DOI: https://doi.org/10.1007/978-3-030-92672-4

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-030-92671-7Published: 15 April 2022

  • Softcover ISBN: 978-3-030-92674-8Published: 16 April 2023

  • eBook ISBN: 978-3-030-92672-4Published: 14 April 2022

  • Series ISSN: 1613-7736

  • Series E-ISSN: 1860-0816

  • Edition Number: 1

  • Number of Pages: VIII, 565

  • Number of Illustrations: 44 b/w illustrations, 240 illustrations in colour

  • Topics: Mechanical Engineering, Computational Science and Engineering, Solid Mechanics

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