A frictionless contact problem for viscoelastic materials
Journal of Applied Mathematics, Volume 2, Issue 1, Page 1-21, 2002., 2002 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.
Mikäel Barboteu +2 more
wiley +1 more source
Optimal boundary control of a viscous Cahn-Hilliard system with dynamic boundary condition and double obstacle potentials [PDF]
, 2014 In this paper, we investigate optimal boundary control problems for Cahn-Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator.
Colli, Pierluigi +3 more
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Optimal velocity control of a convective Cahn-Hilliard system with double obstacles and dynamic boundary conditions: a `deep quench' approach [PDF]
, 2017 In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid ...
Colli, Pierluigi +2 more
core +3 more sources
Weak imposition of Signorini boundary conditions on the boundary element method [PDF]
, 2020 We derive and analyse a boundary element formulation for boundary conditions involving inequalities. In particular, we focus on Signorini contact conditions.
Burman, Erik +2 more
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Analysis of the modified mass method for the dynamic Signorini problem with Coulomb friction [PDF]
, 2011 International audienceThe aim of the present work is to analyze the modified mass method for the dynamic Signorini problem with Coulomb friction. We prove that the space semi-discrete problem is equivalent to an upper semi-continuous one-sided Lipschitz ...
Doyen, David, Ern, Alexandre
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Verification of functional a posteriori error estimates for obstacle problem in 1D [PDF]
, 2008 We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived.
Braess, Dietrich +2 more
core +10 more sources
A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces [PDF]
, 2010 International audienceWe investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the mini- mization problem.
Doyen, David +2 more
core +4 more sources
Coupling of Finite and Boundary Elements for Singularly Nonlinear Transmission and Contact Problems [PDF]
, 2023 This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for interface problems in nonlinear elasticity.
Gimperlein, Heiko, Stephan, Ernst P.
core +2 more sources
Partial constraint singularities in elastic rods
, 2018 We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions.
Hanna, J. A., Singh, H., Virga, E. G.
core +1 more source
A nonsmooth optimization approach for hemivariational inequalities with applications to contact mechanics [PDF]
, 2021 In this paper we introduce an abstract nonsmooth optimization problem and prove existence and uniqueness of its solution. We present a numerical scheme to approximate this solution.
Jureczka, Michał, Ochal, Anna
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