Numerical algorithms for the simulation of finite plasticity with microstructures

C. Carstensen, D. Gallistl, B. Krämer

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-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 languageEnglish
Title of host publicationAnalysis and computation of microstructure in finite plasticity
EditorsS. Conti, K. Hackl
PublisherSpringer
Chapter1
Pages1-30
Number of pages30
ISBN (Electronic)978-3-319-18242-1
ISBN (Print)978-3-319-18241-4
DOIs
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameLecture Notes in Applied and Computational Mechanics
PublisherSpringer
Volume78

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  • Cite this

    Carstensen, C., Gallistl, D., & Krämer, B. (2015). Numerical algorithms for the simulation of finite plasticity with microstructures. In S. Conti, & K. Hackl (Eds.), Analysis and computation of microstructure in finite plasticity (pp. 1-30). (Lecture Notes in Applied and Computational Mechanics; Vol. 78). Springer. https://doi.org/10.1007/978-3-319-18242-1_1