Quasistatic frictional problems for elastic and viscoelastic materials

Oanh Chau; Dumitru Motreanu; Mircea Sofonea

Applications of Mathematics (2002)

  • Volume: 47, Issue: 4, page 341-360
  • ISSN: 0862-7940

Abstract

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We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational inequalities and fixed-point arguments. We also prove that the solution of the viscoelastic problem converges to the solution of the corresponding elastic problem, as the viscosity tensor converges to zero. Finally, we describe a number of concrete contact and friction conditions to which our results apply.

How to cite

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Chau, Oanh, Motreanu, Dumitru, and Sofonea, Mircea. "Quasistatic frictional problems for elastic and viscoelastic materials." Applications of Mathematics 47.4 (2002): 341-360. <http://eudml.org/doc/33119>.

@article{Chau2002,
abstract = {We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational inequalities and fixed-point arguments. We also prove that the solution of the viscoelastic problem converges to the solution of the corresponding elastic problem, as the viscosity tensor converges to zero. Finally, we describe a number of concrete contact and friction conditions to which our results apply.},
author = {Chau, Oanh, Motreanu, Dumitru, Sofonea, Mircea},
journal = {Applications of Mathematics},
keywords = {elastic material; viscoelastic material; frictional contact; evolution variational inequality; fixed point; weak solution; approach to elasticity; subdifferential boundary conditions; penalized or two-sided contact condition; friction; viscoelastic material; elastic material; quasistatic variational inequality; weak solution},
language = {eng},
number = {4},
pages = {341-360},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Quasistatic frictional problems for elastic and viscoelastic materials},
url = {http://eudml.org/doc/33119},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Chau, Oanh
AU - Motreanu, Dumitru
AU - Sofonea, Mircea
TI - Quasistatic frictional problems for elastic and viscoelastic materials
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 4
SP - 341
EP - 360
AB - We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational inequalities and fixed-point arguments. We also prove that the solution of the viscoelastic problem converges to the solution of the corresponding elastic problem, as the viscosity tensor converges to zero. Finally, we describe a number of concrete contact and friction conditions to which our results apply.
LA - eng
KW - elastic material; viscoelastic material; frictional contact; evolution variational inequality; fixed point; weak solution; approach to elasticity; subdifferential boundary conditions; penalized or two-sided contact condition; friction; viscoelastic material; elastic material; quasistatic variational inequality; weak solution
UR - http://eudml.org/doc/33119
ER -

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