Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids

Carsten Carstensen; Petr Plecháč

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 5, page 865-878
  • ISSN: 0764-583X

Abstract

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This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm for efficient discretization. The proposed scheme enables numerical simulations which show that the model allows for hysteresis.

How to cite

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Carstensen, Carsten, and Plecháč, Petr. "Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids." ESAIM: Mathematical Modelling and Numerical Analysis 35.5 (2010): 865-878. <http://eudml.org/doc/197540>.

@article{Carstensen2010,
abstract = { This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm for efficient discretization. The proposed scheme enables numerical simulations which show that the model allows for hysteresis. },
author = {Carstensen, Carsten, Plecháč, Petr},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Variational problems; phase transitions; elasticity; hysteresis; a priori error estimates; a posteriori error estimates; adaptive algorithms; non-convex minimization; microstructure.; variational formulation; two-phase solids; elastic solids; hysteresis; rate-independent phase transformations; a posteriori error estimates; implicit time discretization; microstructure; quasioptimal spatial approximation of stress field; finite element method; a priori error estimates; adaptive mesh-refining algorithm},
language = {eng},
month = {3},
number = {5},
pages = {865-878},
publisher = {EDP Sciences},
title = {Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids},
url = {http://eudml.org/doc/197540},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Carstensen, Carsten
AU - Plecháč, Petr
TI - Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 5
SP - 865
EP - 878
AB - This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm for efficient discretization. The proposed scheme enables numerical simulations which show that the model allows for hysteresis.
LA - eng
KW - Variational problems; phase transitions; elasticity; hysteresis; a priori error estimates; a posteriori error estimates; adaptive algorithms; non-convex minimization; microstructure.; variational formulation; two-phase solids; elastic solids; hysteresis; rate-independent phase transformations; a posteriori error estimates; implicit time discretization; microstructure; quasioptimal spatial approximation of stress field; finite element method; a priori error estimates; adaptive mesh-refining algorithm
UR - http://eudml.org/doc/197540
ER -

References

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