Time-Space FE-PDAS Method for Dynamic Unilateral Contact Problem in Viscoelasticity

2008 ◽  
pp. 707-719
Author(s):  
Jiří Nedoma ◽  
Josef Daněk
Keyword(s):  
Contact Problem ◽  
Unilateral Contact ◽  
Time Space

Tykhonov well-posedness of a frictionless unilateral contact problem

2019 ◽  
Vol 25 (6) ◽  
pp. 1294-1311 ◽  
Author(s):  
Zhenhai Liu ◽  
Mircea Sofonea ◽  
Yi-bin Xiao
Keyword(s):  
Contact Problem ◽  
Variational Formulation ◽  
Unilateral Contact ◽  
Well Posedness ◽  
Unilateral Constraints ◽  
The Family ◽  
Contact Models ◽  
Mechanical Interpretation ◽  
Well Posed ◽  
Natural Way

We consider a frictionless contact problem, Problem [Formula: see text], for elastic materials. The process is assumed to be static and the contact is modelled with unilateral constraints. We list the assumptions on the data and derive a variational formulation of the problem, Problem [Formula: see text]. Then we consider a perturbation of Problem [Formula: see text], which could be frictional, governed by a small parameter [Formula: see text]. This perturbation leads in a natural way to a family of sets [Formula: see text]. We prove that Problem [Formula: see text] is well-posed in the sense of Tykhonov with respect to the family [Formula: see text]. The proof is based on arguments of monotonicity, pseudomonotonicity and various estimates. We extend these results to a time-dependent version of Problem [Formula: see text]. Finally, we provide examples and mechanical interpretation of our well-posedness results, which, in particular, allow us to establish the link between the weak solutions of different contact models.

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