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Numerical Algorithms for the Simulation of Finite Plasticity with Microstructures

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Analysis and Computation of Microstructure in Finite Plasticity

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 78))

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Abstract

This article reports on recent developments in the analysis of finite element methods for nonlinear PDEs with enforced microstructures. The first part studies the convergence of an adaptive finite element scheme for the two-well problem in elasticity. The analysis is based on the relaxation of the classical model energy by its quasiconvex envelope. The second part aims at the computation of guaranteed lower energy bounds for the two-well problem with nonconforming finite element methods that involve a stabilization for the discrete linear Green strain tensor. The third part of the paper investigates an adaptive discontinuous Galerkin method for a degenerate convex problem from topology optimization and establishes some equivalence to nonconforming finite element schemes.

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Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099, Berlin, Germany

    Carsten Carstensen & Boris Krämer

  2. Institut für Numerische Simulation, Universität Bonn, Wegelerstraße 6, D-53115, Bonn, Germany

    Dietmar Gallistl

Authors
  1. Carsten Carstensen
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Correspondence to Carsten Carstensen .

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Editors and Affiliations

  1. Inst. für Angewandte Mathematik, Universität Bonn, Bonn, Germany

    Sergio Conti

  2. Lehrstuhl für Mechanik - Materialtheorie, Ruhr-Universität Bochum, Bochum, Nordrhein-Westfalen, Germany

    Klaus Hackl

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Carstensen, C., Gallistl, D., Krämer, B. (2015). Numerical Algorithms for the Simulation of Finite Plasticity with Microstructures. In: Conti, S., Hackl, K. (eds) Analysis and Computation of Microstructure in Finite Plasticity. Lecture Notes in Applied and Computational Mechanics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-18242-1_1

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  • DOI: https://doi.org/10.1007/978-3-319-18242-1_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18241-4

  • Online ISBN: 978-3-319-18242-1

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