Analytical results on a model for damaging in domains and interfaces*

Elena Bonetti; Michel Frémond

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 4, page 955-974
  • ISSN: 1292-8119

Abstract

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This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable variational formulation) of the related Cauchy problem by means of a Schauder fixed point argument, combined with monotonicity and compactness tools. We also perform an asymptotic analysis of the solutions as the interfacial damage energy (between the body and the contact surface) goes to +∞.

How to cite

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Bonetti, Elena, and Frémond, Michel. "Analytical results on a model for damaging in domains and interfaces*." ESAIM: Control, Optimisation and Calculus of Variations 17.4 (2011): 955-974. <http://eudml.org/doc/221915>.

@article{Bonetti2011,
abstract = { This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable variational formulation) of the related Cauchy problem by means of a Schauder fixed point argument, combined with monotonicity and compactness tools. We also perform an asymptotic analysis of the solutions as the interfacial damage energy (between the body and the contact surface) goes to +∞. },
author = {Bonetti, Elena, Frémond, Michel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Damage; contact; adhesion; existence; asymptotic analysis; initial-boundary value problem; internal constraints; Schauder fixed point argument},
language = {eng},
month = {11},
number = {4},
pages = {955-974},
publisher = {EDP Sciences},
title = {Analytical results on a model for damaging in domains and interfaces*},
url = {http://eudml.org/doc/221915},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Bonetti, Elena
AU - Frémond, Michel
TI - Analytical results on a model for damaging in domains and interfaces*
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2011/11//
PB - EDP Sciences
VL - 17
IS - 4
SP - 955
EP - 974
AB - This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable variational formulation) of the related Cauchy problem by means of a Schauder fixed point argument, combined with monotonicity and compactness tools. We also perform an asymptotic analysis of the solutions as the interfacial damage energy (between the body and the contact surface) goes to +∞.
LA - eng
KW - Damage; contact; adhesion; existence; asymptotic analysis; initial-boundary value problem; internal constraints; Schauder fixed point argument
UR - http://eudml.org/doc/221915
ER -

References

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