A frictionless contact problem for viscoelastic materials
We consider a mathematical model which describes the contact between a deformable body and an obstacle, the so-called foundation. The body is assumed to have a viscoelastic behavior that we model with the Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the well-known...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X02000219 |
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| Summary: | We consider a mathematical model which describes the contact
between a deformable body and an obstacle, the so-called
foundation. The body is assumed to have a viscoelastic behavior
that we model with the Kelvin-Voigt constitutive law. The contact
is frictionless and is modeled with the well-known Signorini
condition in a form with a zero gap function. We present
two alternative yet equivalent weak formulations of the problem
and establish existence and uniqueness results for both
formulations. The proofs are based on a general result on
evolution equations with maximal monotone operators. We then
study a semi-discrete numerical scheme for the problem, in terms
of displacements. The numerical scheme has a unique solution. We
show the convergence of the scheme under the basic solution
regularity. Under appropriate regularity assumptions on the
solution, we also provide optimal order error estimates. |
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| ISSN: | 1110-757X 1687-0042 |