# Analysis of a viscoelastic antiplane contact problem with slip-dependent friction

Thierry-Vincent Hoarau-Mantel; Andaluzia Matei

International Journal of Applied Mathematics and Computer Science (2002)

- Volume: 12, Issue: 1, page 51-58
- ISSN: 1641-876X

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topHoarau-Mantel, Thierry-Vincent, and Matei, Andaluzia. "Analysis of a viscoelastic antiplane contact problem with slip-dependent friction." International Journal of Applied Mathematics and Computer Science 12.1 (2002): 51-58. <http://eudml.org/doc/207568>.

@article{Hoarau2002,

abstract = {We study a mathematical problem modelling the antiplane shear deformation of a viscoelastic body in frictional contact with a rigid foundation. The contact is bilateral and is modelled with a slip-dependent friction law. We present the classical formulation for the antiplane problem and write the corresponding variational formulation. Then we establish the existence of a unique weak solution to the model, by using the Banach fixed-point theorem and classical results for elliptic variational inequalities. Finally, we prove that the solution converges to the solution of the corresponding elastic problem as the viscosity converges to zero.},

author = {Hoarau-Mantel, Thierry-Vincent, Matei, Andaluzia},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {viscoelastic law; slip-dependent friciotn law; antiplane problem; convergence; vanishing viscosity; antiplane shear deformation; classical formulation; variational formulation; existence; unique weak solution; Banach fixed-point theorem; elliptic variational inequalities},

language = {eng},

number = {1},

pages = {51-58},

title = {Analysis of a viscoelastic antiplane contact problem with slip-dependent friction},

url = {http://eudml.org/doc/207568},

volume = {12},

year = {2002},

}

TY - JOUR

AU - Hoarau-Mantel, Thierry-Vincent

AU - Matei, Andaluzia

TI - Analysis of a viscoelastic antiplane contact problem with slip-dependent friction

JO - International Journal of Applied Mathematics and Computer Science

PY - 2002

VL - 12

IS - 1

SP - 51

EP - 58

AB - We study a mathematical problem modelling the antiplane shear deformation of a viscoelastic body in frictional contact with a rigid foundation. The contact is bilateral and is modelled with a slip-dependent friction law. We present the classical formulation for the antiplane problem and write the corresponding variational formulation. Then we establish the existence of a unique weak solution to the model, by using the Banach fixed-point theorem and classical results for elliptic variational inequalities. Finally, we prove that the solution converges to the solution of the corresponding elastic problem as the viscosity converges to zero.

LA - eng

KW - viscoelastic law; slip-dependent friciotn law; antiplane problem; convergence; vanishing viscosity; antiplane shear deformation; classical formulation; variational formulation; existence; unique weak solution; Banach fixed-point theorem; elliptic variational inequalities

UR - http://eudml.org/doc/207568

ER -

## References

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