Numerical analysis of a relaxed variational model of hysteresis in two-phase solids

Carsten Carstensen; Petr Plecháč

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • 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 - Modélisation Mathématique et Analyse Numérique 35.5 (2001): 865-878. <http://eudml.org/doc/194077>.

@article{Carstensen2001,
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 - Modélisation Mathématique et Analyse Numérique},
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; rate-independent phase transformations; implicit time discretization; quasioptimal spatial approximation of stress field; finite element method; adaptive mesh-refining algorithm},
language = {eng},
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/194077},
volume = {35},
year = {2001},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2001
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; rate-independent phase transformations; implicit time discretization; quasioptimal spatial approximation of stress field; finite element method; adaptive mesh-refining algorithm
UR - http://eudml.org/doc/194077
ER -

References

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