A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies

Alice Fiaschi

ESAIM: Control, Optimisation and Calculus of Variations (2009)

  • Volume: 15, Issue: 2, page 245-278
  • ISSN: 1292-8119

Abstract

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Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms of stochastic processes on a suitable probability space.

How to cite

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Fiaschi, Alice. "A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies." ESAIM: Control, Optimisation and Calculus of Variations 15.2 (2009): 245-278. <http://eudml.org/doc/245433>.

@article{Fiaschi2009,
abstract = {Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms of stochastic processes on a suitable probability space.},
author = {Fiaschi, Alice},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {quasistatic evolution; rate-independent processes; elastic materials; incremental problems; Young measures; existence; stochastic processes; probability space},
language = {eng},
number = {2},
pages = {245-278},
publisher = {EDP-Sciences},
title = {A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies},
url = {http://eudml.org/doc/245433},
volume = {15},
year = {2009},
}

TY - JOUR
AU - Fiaschi, Alice
TI - A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2009
PB - EDP-Sciences
VL - 15
IS - 2
SP - 245
EP - 278
AB - Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms of stochastic processes on a suitable probability space.
LA - eng
KW - quasistatic evolution; rate-independent processes; elastic materials; incremental problems; Young measures; existence; stochastic processes; probability space
UR - http://eudml.org/doc/245433
ER -

References

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