Numerical algorithms for the simulation of finite plasticity with microstructures

C. Carstensen; D. Gallistl; B. Krämer

doi:10.1007/978-3-319-18242-1_1

Numerical algorithms for the simulation of finite plasticity with microstructures

C. Carstensen, D. Gallistl, B. Krämer

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

1 Citation (Scopus)

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.

Original language	English
Title of host publication	Analysis and computation of microstructure in finite plasticity
Editors	S. Conti, K. Hackl
Publisher	Springer
Chapter	1
Pages	1-30
Number of pages	30
ISBN (Electronic)	978-3-319-18242-1
ISBN (Print)	978-3-319-18241-4
DOIs	https://doi.org/10.1007/978-3-319-18242-1_1
Publication status	Published - 2015
Externally published	Yes

Publication series

Name	Lecture Notes in Applied and Computational Mechanics
Publisher	Springer
Volume	78

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10.1007/978-3-319-18242-1_1

Cite this

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title = "Numerical algorithms for the simulation of finite plasticity with microstructures",

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.",

author = "C. Carstensen and D. Gallistl and B. Kr{\"a}mer",

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doi = "10.1007/978-3-319-18242-1_1",

language = "English",

isbn = "978-3-319-18241-4",

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Numerical algorithms for the simulation of finite plasticity with microstructures. / Carstensen, C.; Gallistl, D.; Krämer, B.
Analysis and computation of microstructure in finite plasticity. ed. / S. Conti; K. Hackl. Springer, 2015. p. 1-30 (Lecture Notes in Applied and Computational Mechanics; Vol. 78).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Numerical algorithms for the simulation of finite plasticity with microstructures

AU - Carstensen, C.

AU - Gallistl, D.

AU - Krämer, B.

PY - 2015

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AB - 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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M3 - Chapter

SN - 978-3-319-18241-4

T3 - Lecture Notes in Applied and Computational Mechanics

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BT - Analysis and computation of microstructure in finite plasticity

A2 - Conti, S.

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PB - Springer

ER -

Numerical algorithms for the simulation of finite plasticity with microstructures

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