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.
@article{bwmeta1.element.bwnjournal-article-amcv12i1p51bwm,
author = {Hoarau-Mantel, Thierry-Vincent and Matei, Andaluzia},
title = {Analysis of a viscoelastic antiplane contact problem with slip-dependent friction},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {12},
year = {2002},
pages = {51-58},
zbl = {1038.74032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv12i1p51bwm}
}
Hoarau-Mantel, Thierry-Vincent; Matei, Andaluzia. Analysis of a viscoelastic antiplane contact problem with slip-dependent friction. International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) pp. 51-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv12i1p51bwm/
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